How Black is a Black Hole? An Introduction to the Paradoxes

Following on Thursday’s post and yesterday’s about black holes, specifically about Hawking’s recent vague proposal that was so widely (but rather misleadingly) reported in the media, and about the back-story which explains why there’s so much confusion about black holes among scientists interested in quantum gravity, and why Hawking made his suggestion in the first place, I’ve been motivated to write up a new introduction to the black hole information paradox.  This should provide the basic knowledge and the context that I’m sure many of you are looking for.  Please take a look and send comments!

11 responses to “How Black is a Black Hole? An Introduction to the Paradoxes

  1. Hi Matt,
    Has Hawking lost his credibility among his peers? I heard a couple Nobel Prize winning physicists interviewed the other day and when asked about a few statements Hawking had made recently, their response was “well, that’s Stephan”. I got the impression my hero’s relevance is slipping.

    • It’s something in between the media reverence and what you suggest. Hawking has always been relevant and commands high respect, but his most important work was done in the 1970s. It is rare for even a great physicist to make a long series of contributions that last his or her entire career. Einstein’s last 30 years added up to nothing; of course the first 20 years changed everything, so who cares? So it’s far too strong to suggest that he’s dismissed by his colleagues, but it would also be far too strong to imagine people dwell on his every word. He’s a highly respected member of a community, but he’s one of many highly-respected people, and just because he’s famous for his 40-year-old work doesn’t mean that everything he says today is correct. This respected-but-not-worshipped status has been true of many other great physicists in the past.

      • Carl 'SAI' Mitchell

        I think it also shows an effect particular to the sciences and math: people respect others enough to talk openly about their flawed or incomplete arguments. Physicists aren’t going to be sycophants to Hawking, they’re going to treat him like a physicist and evaluate his ideas on their merits. Likewise Hawking respects the physics community, and clearly welcomes people working on and criticizing his ideas. He’s not going to assume people will take what he says on faith, he’s going to want others to help examine the ideas, find flaws, and form them into a consistent set of equations.

        Outside of science/math most people consider telling someone they’re wrong or asking for evidence of a statement to be at least somewhat rude. Inside it’s standard procedure, and someone who blindly accepts new propositions will be considered gullible at best.

  2. One thing I’ve been wondering about: Seen from the outside, the evaporation of a black hole is exceedingly slow. For an observer well inside the (apparent) horizon, though, can’t the process seem arbitrarily fast due to gravitational time dilation? As a layperson it’s intriguing to imagine what this would “look like”, though I have no idea whether the question has any real merit.

    • This is complicated, because time is a wacky thing in general relativity. For example, it will be very different for an observer who goes flying into the strongly curved region of the black hole, where general relativity says there’s a singularity (but which probably isn’t so singular in the real quantum theory of gravity), as opposed to an observe who fires up a powerful rocket and is able to stay away from the singularity for a while. In any case, the person inside the horizon is destroyed somehow before evaporation is complete. I haven’t calculated the minimum time this would appear to take, but one could do that; I don’t think one could calculate the maximum apparent time because it would depend on the precise way that destruction of the observer and evaporation of the black hole conclude, and these aren’t known.

  3. Curious George

    These are exciting problems, but maybe not fully realistic – I’m only saying that we should consider them in a perspective. There used to be an old good Newton’s system, elegant, and consistent. Then it was found that it did not describe electromagnetic fields (or high-velocity objects) properly, and a special relativity was born. It is elegant, and consistent; Maybe it has limits, too. A general relativity allows for singular solutions, and we are seriously stretching the equations – in a sense, to infinity. Maybe there are limits to this elegant and consistent theory, too. There are cracks already appearing – we have to postulate dark matter and dark energy to obtain an agreement with observation.

  4. Scientific theories are tools, and like all tools do, they have a scope.

    Tools work well within their scope, but get lousier results when they are used further away from their scope. This problem of the scope of tools is very well described by that popular phrase: “When all I have is a hammer, everything looks like a nail”, and you can imagine somebody banging a screw with a hammer.

    Scientific theories have a scope, and they work well and can give a proper description of nature for regimes within the scope of said theory.

  5. I read the following question in a forum

    “something has always struck me as fishy with these black holes. If they are so unstable as to evaporate by Hawkins radiation, it seems to me they should not form in the first place. The Hawkins radiation should already appear during their collapse, and prevent it.”

    what is the answer to this ?

    • The time to form a black hole via, say, the collapse of a star is a few seconds. The time for such a black hole to evaporate is longer than the lifetime of the universe.

      Even though water evaporates in sunlight, that does not prevent you from pouring water on the ground and making a puddle. The former takes much longer than the latter.

      That said, if you make a puddle that’s just a few atoms, it may evaporate as quickly as you form it. And a tiny black hole can evaporate on very short time scales, too.

      But big ones evaporate much more slowly than they can form.

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