Of Particular Significance

Did Hawking Say “There Are No Black Holes”?

POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 01/30/2014

Media absurdity has reached new levels of darkness with the announcement that Stephen Hawking has a new theory in which black holes do not exist after all.

No, he doesn’t.

[Note added: click here for my new introduction to the black hole information paradox.]

First, Hawking does not have a new theory… at least not one he’s presented. You can look at his paper here — two pages (pdf), a short commentary that he gave to experts in August 2013 and wrote up as a little document — and you can see it has no equations at all. That means it doesn’t qualify as a theory. “Theory”, in physics, means: a set of equations that can be used to make predictions for physical processes in a real or imaginary world. When we talk about Einstein’s theory of relativity, we’re talking about equations. Compare just the look and feel of Hawking’s recent note to Einstein’s 1905 paper on the theory of special relativity, or to Hawking’s most famous 1975 paper on black holes; you can easily see the difference without understanding the content of the papers.

The word “theory” does not mean “speculations” or “ideas”, which is all that is contained in this little article. Maybe that’s what theory means at a cocktail party, but it’s not what “theory” means in physics.

Second, what Hawking is addressing in this note is the precise level of blackness of a black hole… in short, whether the name “black hole” for the objects we call black holes is really appropriate. But simply the fact that black holes aren’t quite black isn’t new. In fact it was Hawking himself who became famous in 1974-1975 for pointing out that in a world with quantum physics, typical black holes cannot be precisely black — so it’s not true that nothing ever comes out of a black hole. Black holes must slowly radiate elementary particles, a process we call Hawking radiation.

From day 1, Hawking’s observation posed puzzles about how conflicting requirements of quantum theory and Einstein’s gravity would be resolved, with quantum theory demanding that all information that fell into the black hole be neither destroyed nor copied, and Einstein’s gravity insisting that there is no way that the information of what went into a black hole can ever come out again, even if the black hole evaporates and disappears. The assumption of the community has long been that the 1970s calculation that Hawking did, while largely correct, leaves out a small, subtle effect that resolves the puzzle. The question is: what is the nature of that subtle effect?

No one, including Hawking, has posed a satisfactory answer. And that is why we keep hearing about black holes again and again over the decades, most recently in the context of the “firewall paradox”. In his recent paper, Hawking, like many of his colleagues, is proposing another possible answer, though without demonstrating mathematically that his proposal is correct.

But did Hawking really say “There are no black holes”, or didn’t he??

Talk about taking things out of context!!! Here’s what Hawking actually said.

First he suggests that the edge of a black hole — called its “event horizon”, a very subtle concept when you get into the details — really isn’t so sharp once quantum effects are considered. Many people have suggested one version or another of this possibility, which would represent a small but critical correction to what Hawking said in the 1970s (and to what people understood about black holes even earlier).

And then Hawking writes…

“The absence of event horizons mean that there are no black holes – in the sense of regimes from which light can’t escape to infinity.”

Notice the final clause, which is omitted from the media reports, and is absolutely necessary to make sense of his remark. What he means is that black holes are very, very slightly (though importantly) less black than he said in his 1974 paper… because the things that fall into the black hole do in some sense eventually come back out as the black hole evaporates. I say “in some sense” because they come out thoroughly scrambled; you, for example, if you fell in, would not come back out, even though some of the elementary particles out of which you are made might eventually do so.

And then he says

“There are however apparent horizons which persist for a period of time.”

Translation: for an extremely long time, what we call a black hole will behave in just the way we have long thought it does. In particular, there is no change in any of the astrophysics of black holes that astronomers have been studying in recent decades. The only issue is what happens as a black hole begins to evaporate in a serious way, and when you look very, very carefully at the details of the Hawking radiation, which is very difficult to do.

“This suggests that black holes should be redefined as metastable bound states of the gravitational field.”

In short: In Hawking’s proposal, it’s not that the objects that you and I would call “black holes” don’t exist!  They are still there, just with a new name, doing what we’ve been taught they do except in some fine-grained detail. Not that this fine-grained detail is unimportant — it’s essential to resolving the quantum vs. gravity puzzle.  But an ordinary person watching or exploring near a black hole would notice no difference.

Notice also all of this is a proposal, made in words; he has not shown this with mathematics.

In short, although Hawking is, with many of his colleagues, working hard to resolve the puzzles that seem to make quantum theory conflict with Einstein’s theory of gravity in this context, he’s not questioning whether black holes exist in the sense that you and I would mean it. He’s addressing the technical issue of exactly how black they are, and how the information contained in the things that fall in comes back out again. And since he’s just got words, but not math, to back up his suggestions, he’s not convinced his colleagues.

Meanwhile, the media takes the five words “There Are No Black Holes” and creates almost pure fiction, fiction that has almost nothing to do with the reality of the science. Well done, media, well done. Sometimes you’re just like a black hole: information comes in, and after being completely scrambled beyond recognition, comes back out again through a mysterious process that makes no sense to anyone. Except that in your case, it’s very clear that information is lost, and misinformation is created.

Hey! That’s a new theory of black holes! (I’ll write a 2-page paper on that this afternoon…)

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  10. A very interesting article. Thanks. Sadly the media always pick up on the most sensationalist aspects of a story, even if it means taking quotes out of context or leaving important parts of them out. They are trying to create interest in their stories, not necessarily to report in a balanced or objective way.

  11. Reblogged this on In the Dark and commented:
    Last week there was a rather tedious flurry of media activity about Stephen Hawking’s alleged claim that there are no black holes after all. Here’s a nice blog post explaining what Hawking actually said. Also, check out the link at the start of this article to a very nice layperson’s guide to the Black Hole Information Paradox.

  12. I am not sure why, but Hawking has assumed that BH are living in asymptotically flat AdS space (instead of physical, dS ones), so he uses AdS/CFT + CPT arguments to conclude that no BH can exist. Well, the whole trouble concerning physical BH is that they are embedded in dS spacetimes not in AdS ones. This simply throws the baby out with the bath water …

    1. The reason Hawking discusses this is that a sufficiently small black hole is insensitive to the AdS (“Anti-de Sitter”) boundary conditions. Therefore, the physics of a black hole being created and evaporating in flat space is the same, to a very good approximation, as that of one being created and evaporating in Anti-de Sitter space, as long as the black hole is small compared to the curvature radius of the AdS space. That’s why he (and many others) can address the information paradox in this context.

      At least this is the wide consensus. At this point, if you made an argument to the contrary in public, you’d be asked to show evidence that a black hole in flat space or in de Sitter space is fundamentally different from a small one in Anti de Sitter space. No one has given such evidence, and the experts think there isn’t any to be given.

      1. Well, hence gravity is a long-range force it is not granted that one can use arguments like yours: “sufficiently small black hole”. For instance just check: Microcanonical Thermodynamics: Phase Transitions in “small” Systems, Dieter H. E. Gross, World Scientific, 2001 to understand implications for phase transitions (as the formation/evaporation of BH). At this point, boundary conditions do become relevant for defining the fate of a metastable thermodynamic system!

        On the other hand, it is well-known that AdS (in contradistinction to dS) is not a globally hyperbolic spacetime. In non-globally hyperbolic manifolds knowledge of equations of motion and of initial data is not enough to determine the time evolution of physical quantities. In the anti-de Sitter case, the lack of global hyperbolicity is due to **the existence of a boundary at spacelike infinity**: information can flow in from infinity.

          1. Well, actually I don’t need, after Lynden-Bell work for ordinary stars in the 70’s: http://articles.adsabs.harvard.edu//full/1977MNRAS.181..405L/0000405.000.html. You just have to remember that boundary conditions are important for defining the thermodynamics of long-range interactive systems when (if) taking the thermodynamic limit. If you disagree, after reading those references, disprove it!

            1. It’s not up to me; you have to convince Hawking, Susskind, Maldacena, Polchinski, Horowitz, etc. — in short, the real experts on this subject. If there were subtleties that would invalidate what I told you, I wouldn’t be able to check it myself. However, I don’t think you got the point. Everyone knows boundary conditions are important. But you have to show that these problems you mention are actually enough to invalidate the argument concerning small black holes in AdS. They may be important for some things, but still not dominant for the question at hand.

              I’ve heard dozens of complaints about all of the arguments that people are making. Give me a calculation, not words; I’m done with words.

  13. Matt you say “If quantum theory is true, then information cannot be lost. It’s fundamental to the mathematics of the theory”. So you reject von Neumann’s concept of collapse of the wave function, where information is indeed lost: the state before collapse cannot be determined from the eigenstate afterwards.
    What do you suggest takes its place? How does the wave function attain its physical meaning in terms of realised classical states that obey Born-rule probabilities? And how does one determine the quantum state before a measurement is made from the state after it has been made?

  14. Truly. This Mr. Savorinen has been a nuisance in Finland for a decade or so. We all in Finland are not that stupid.

  15. Mr. Savorinen seems like a pseudonym for one Mr. Kauko Nieminen, who explains the structure of matter and the origin of the universe in a seminal book that, to the unprepared eye, looks like a collage of newspaper clippings, pencil-drawn diagrams and mystical explanations. The campus bookstore even carried it, apparently just for the kicks.

    Sorry on behalf of the Finns, remember also Nordström…

    1. I don’t know mr. Savorinen personally, but based on his writings in Finnish “science” forums he has good manners and good intentions. Those are good virtues for all of us. I’m proud to be Finnish 🙂

  16. Outside of this article, I have not heard of the existence of media reports giving people the impression that Hawking denied the existence of black hole–like objects. I was aware, via Twitter, of some dumb comments made by a person with the initials M.B. who has for several years now been disqualified from entering the Being Deliberately Stupid competition on the grounds that other contestants should have a chance, but that is not the media’s fault.

  17. In AWT the Hawking is both correct, both wrong. The black holes are massive dense stars with both physical surface (i.e. firewall), both event horizon. Sometimes the physical surface extends the horizon and it makes the black hole radiative (mostly at poles). Therefore the black holes can evaporate their matter with age much faster, than Hawking radiation allows, but this speed of evaporation slows down with age.

  18. Hello Matt. I think, i already found out how universe really work!

    For me space is eternal, infinity place and it is nothing! Space dont expanding or curving or changing at all!

    There is some concrete thing “who” is always pushing some direction and there is densers “who” recycling that concrete thing.

    In visible universe densers recycling that thing “who” expanding all a atime and thats why quarks and photons expanding all a time.

    So, space dont expanding! We expanding in space “who” dont expanding!

    Also “black holes” expanding and inside expanding “black holes” pushing outside expanding densers / particle “who” are so density, that our expanding machine cant register this densers!

    All expanding atoms are from galaxys centre expanding supermassive concentration!

    Expanding photons are from expanding nucleus of atoms!

    I write some with my mother language.

    Atomien ytimet kierrättävät koko ajan laajenevaa asiaa tihentymiä joista voi syntyä / yhdistyä uusia elektroneja tai fotoneita!.

    Vain pienestä osasta näistä tihentymistä joita työntyy ulos atomien ytimistä, yhdistyy elektroneja tai fotoneita!

    Galaksien keskusten supermassiivisista keskittymistä ulos työntyvistä tihentymistä vain pienestä osasta syntyy havaittavaa ainetta ja vielä pienemmästä osasta yhdistyy uusia tähtiä!

    Galakisen keskusten supermassiiviset keskittymät ovat yhdistyneet vastaavalla tavalla erittäin massiivisista ja tiheistä tihentymistä, kun niiden sisälle on työntynyt ulkoapäin normaalia enemmän liikettä, jolloin erittäin monen erillisen tihentymän sisäinen liike / paine on kasvanut voimakkaasti ja näin erittäin monen tihentymän voimakas kolmiulottiinen laajeneminen isolla alueella kohdistaa tuon alueen keskustaan ison paineen ilman vetävää voimaa jne.


    1. Hello Kimmo. Would you like to translation text what i write next. I explain how stars born with out pulling force and with out curving space!

      Galaksien keskusten supermassiivisista ja erittäin tiheistä kohteista siis työntyy koko ajan ulos tihentymiä joilla on massaa yhtä paljon kuin protoneilla! Ne ovat kuitenkin paljon pienempiä kuin meidän protonit, eli niissä oleva liike on puristuneena paljon pienemmälle alueelle eli se on paljon tiheämmin niissä kuin meidän protoneissa!

      Siksi niiden sisäinen liike / aika on paljon hitaampaa kuin meidän protoneiden sisäinen liike / aika on! Ja juuri siksi meidän laitteet eivät kykene rekisteröimään niitä!

      Ajatellaan tilanne jossa kaksi galaksin keskustan supermassiivista kohdetta ohittaa toisensa läheltä jolloin molemmista ulos työntyvät tihentymät vuorovaikuttavat vastaavien tihentymien kanssa joita niitä vastaan työntyy tiheästi!

      Silloin kyseisiin tihentymiin työntyy ulkoapäin paljon enemmän liikettä joka vooimistaa kyseisten tihentymien sisäistä liikettä / painetta ja näin ne laajenevat voimakkaasti!

      Kun isolla alueella erittäin monet samaan suuntaan työntyvät tihentymät laajenevat kolmiulotteisesti voimakkaasti saman aikaisesti, kohdistuu tuon alueen keskustassa oleviin laajeneviin tihentymiin erittäin voimakas ulkoinen liike / paine / työntävä voima ja näin sieltä vapautuu paljon liikettä fotoneina jotka työntyvät ulos uudesta tähdestä, saaden uutta tähteä kohti liikkuvien tihentymien sisäisen liikkeen voimistumaan ja näin uuden tähden pintakerroksien aineeseen liikettä / työntävää voimaa tähden ulkopuolelta jne!

      And all this with out pulling force or curving space!

      I say alreaydy, thank you Kimmo for my text translation!


        1. No Kimmo. I am not kidding with you!

          Now you have a chance make history!

          You can translate my text!

          I am the one who found out / explained how the universe really works!

          Kimmo, Dont “walk” over your enormous chance!


      1. Ok, this is one time occasion! I happen to be in flow mode 😉

        Jukka said in Finnish that stars will be born by pure hand waving. Faster one waves his hands then faster those stars will emerge. With fast enough waving one will experience pushing “things” which push themselves through one’s waving hands. Eventually one might experience “starlike” sensation 🙂

        This comment was so lame that Matt should delete it.

        1. Kimmo, you funny dude! 😉

          do you know why you can move yours hand?

          You can change your body’s internal motion your body movement in relation destination outside the.

          Voit siis muuttaa kehosi sisäisen liikkeen / energian kehosi liikkeeksi suhteessa kehosi ulkopuolisiin kohteisiin!

          Liike on vastaus kaikkeen!

          Movement is answer for all phenomenas!

          Missä liikettä, siellä tiheydenvaihtelua ja muutosta!


    2. How quarks “who” expanding twice bigger can slow down movement what coming outside to inside quarks? That movement what quarks have, is not so density after that!

      Answer is that! Also that stuff expanding “who” is moving inside quarks “who” expanding!

      Also that stuff “who” moving out from expanding quarks, expanding all a time!

      Thats why everything what expanding quarks have, changing in time!

      Thats the reason why quarks can expanding very long time!

      Guess why material are dynamics?

      Answer is movement!

      Space is not dynamics!

      Space is nothing and space really dont change with time!

      Movement is time!

      If there is no movement, there is no change!

      So, why you believe that space expanding!

      Can you explain how and why space expanding?

      I can explain how and why quarks and photons expanding!


  19. In a way, Hawking’s main contribution has been to show that, considering all that we know, Black Holes are not truly black, ever. So, in a way, he is celebrating himself with a striking formula, it should feed the conversation. Journalists can always be shipped to Sagittarius A*, if they don’t “believe” in BH…

  20. I am no physicist, but I see that you address your blog to interested lay(wo)men as well. 🙂
    I am a little “sad” to somehow lose the singularity of the black hole now since the core of a black hole is now looking less like a singularity in the sense of infinite density and energy). Maybe you answered this in your postings about string theory and maybe the question is stupid altogether – please pardon me in advance. What density does the superstring field have or does a quantum vacuum state have? Was there any relationship between the singularity assumed to be in the core of a black hole till now and maybe the singularity of the quantum vacuum state? Sorry for my uninfomedness. I am a simple educator. Thank you.

  21. Dino,

    The quote from Bondi I regard as one of the most eloquent statements of the ideals of science. A more succinct one is from the astrophysicist Bradley Shaefer:

    “Science advances by exploring unexplored regions and by performing critical tests of standard wisdom.”

    Standard wisdom–repeated in probably hundreds of books and articles and innumerable times every academic semester–is that the result of Galileo’s experiment is simple harmonic motion. In no case that I know of is it ever pointed out that we have no direct empirical evidence to back up the standard answer.

    Doing the experiment, therefore, at the very least, would permit authors and instructors to cite the evidence every time the problem comes up.

    Maybe my suggestion to do Galileo’s experiment is routinely ignored because physicists are embarrassed to admit that this is really a rather large gap in our empirical evidence. Hard to figure out any other reason they so flagrantly disregard their own ideals.

  22. Steven Hawking said what he said. As ‘defined’, by the very terms he used to popularize the subject to the public, black holes as formulated do not exist. There appears to be dense objects with very high gravity in the universe, but the theory behind them or how they might function in relation to known physics is not correct according to Hawking. Now you can accept what he said, and decide to agree or disagree with it. What you can’t do, is continue to pretend you can recast his words into any shape you like. If you can’t even agree with each other what the man said or what it means, how can you look down on the media or general public for being confused or mislead?

  23. V interesting post and interesting discussion. I think you’re right, it is a frightening example of a slight misstatement of a result by the media that leads to an entirely erroneous takeaway message……and let us not forget that such media misunderstandings never die. One can expect members of the audience at public lectures for decades to come to declare “but Hawking says there are no black holes”!
    I was also perturbed at the way media outlets once again attributed many standard ideas in physics to one person (Hawking)….exactly like those glowing reviews of A brief history by journos who seemed to think Hawking had dreamed up our best model of the cosmos….

  24. All the theories predominant in cosmology today are beautiful and magical. It is impossible not to love them to some extent.
    But, there is always but……
    When all them are translated to ordinary language, one can not but ask him/her self: are they for real?
    Obviously I’m not a scientists but I have been reading on the subjects extensively for the last 25 years. And from initial love for the subject I came to the point where I realised that most of the components required to make equations work have been artificially evoked, into existence. And I can’t but to think that this all has gone wrong somewhere…
    I mean, dimensionless points of infinite density? Really?
    It seems to me that someone is just on the right track to make more

    1. “I mean, dimensionless points of infinite density? Really?”

      Nobody knows if “really” because nobody can see inside a black hole to check. It’s simply the prediction of the equations that appear to predict all the behavior *outside* the black hole perfectly. A lot of physicists are uncomfortable with the idea, and it is believed by many that a full quantum understanding of gravity will include something that prevents the singularity from actually forming.

      On the other hand, things that are really, really weird and make no intuitive sense at all and are simply in equations to make them work are as real as anything can ever be said to be real. It’s been almost a hundred years since “I’m uncomfortable with the idea that reality can really work this way because it offends my intuition” has been a reason, on its own, to say something doesn’t really exist.

  25. Concerning this issue and the way it was reported in mass media, The New Yorker has a hilarious piece by Borowitz, about Michele Bachmann “underscor[ing] ‘the danger inherent in listening to scientists'”. Although the article is obviously satyrical, it is so “realistic” that most of my physicist colleagues have been completely taken in.

    Talking about the abysmal levels of journalism absurdity, you should also look at how that simulation of the magnetic monopole at Amherst College has been covered in Italian media, including in la Repubblica (the largest-circulation Italian newspaper)…

  26. Equations are just very precise sentences, nothing more, nothing less. They are not the Golden Calves.

    Equations are crucial to distinguish two exquisitely close theories (as in BH physics). However, exquisitely precise physics can itself become a trap, if the foundations of the theory are wrong.

    The best known example being the geocentric theory, which became a prisoner of its precise mathematics (Fourier analysis in disguise). It took 19 centuries (Kepler) to make the math of heliocentrism precise enough to contradict geocentrism (but Tycho was handsomely financed because he had a hunch that ancient astronomers had cheated, especially about Mars).

    Earlier, Buridan (1320 CE) had contradicted Aristotle, by discovering inertia (“Newton’s First Law”), and pointing out that it made heliocentrism as valid as geocentrism (but for the little problem of “scripture”…. the specialists of which put all of Buridan’s work at the “Index of Prohibited Books”, a century after his death… Although he was part of mandatory teaching in Cracow, where Copernic studied…. thanks to Hus, earlier burned to a crisp, alive, by the highest cardinals).

    Ideas are more general than equations. Equations, like sentences, are written with concepts (root: becoming pregnant)… and pre-conceptions. “Shut up and calculate” goes only that far (my gaze is turning towards “superstrings”).

    With the wrong concepts, it does matter how many equations one writes.

    1. Equations are not just precise sentences, they are precise *quantitative* sentences. Equations are how you figure out if your concepts are right or wrong, by comparing them to empirical reality.

      Without equations, it doesn’t matter whether you think your concepts are “right” or “wrong”. With equations, then if the concepts are sufficiently wrong then it’s the equations that will show that. If the equations do not show that, then what is your basis for saying that the concept is wrong?

      And you’re conflating geocentrism with epicycles. Copernicus’ heliocentric model used epicycles. And the math never became precise enough to disprove epicycles. It only became precise enough to allow Kepler to realize that the epicycles were converging on ellipses. They are ultimately mathematically equivalent, but ellipses are easier to work with and make further inferences from. Without precise equations and data to compare it to, then he wouldn’t have realized this.

      It’s easy for you to sit here with all that history behind us and say that they should have just realized that ellipses were the right concept to begin with, but it’s only obvious to you because of the precise math that went into showing that this was indeed the right concept to describe reality.

      For things where we don’t already know the right answer, then equations are how you figure that out. Trying to declare which concept is “right” before working out the equations and seeing if it matches reality is bass-ackwards.

    2. Really, it’d be more correct to say that a sufficiently precise sentences structured in such a way that rigorous logical inferences can be made is math, rather than vice versa.

      1. Anon: I did not say ellipses were easy to figure out. They were not. Kepler tried something like 100 different curves. However, clearly Buridan knew that the heliocentric theory was right. Heliocentrism is no more about ellipses than Kepler’s theory was about the 1/d in gravitation.

        A French astronomer got the 1/dd, and Newton exploited it. The point is, theories have degrees.

        Geometry did without equations until Bolyai and Lobachevsky. Even then, the (re)”discovery” of Non Euclidean geometry was, fist of all, a philosophical phenomenon, the realization that geometry was a local computation, or modelization.

        Riemann’s shattering ideas were in a paper (Habilitationsschrift)… With just one (sort of) equation. His paper was all about concepts, including some erroneously attributed to Einstein. Speaking of Einstein his Special Relativity work of 1905 was just a neat repackaging of what was already known (that means it strictly did not have ONE new equation).

        Considering the history of the last 5,000 years of science, Descartes having invented algebraic geometry less than 4 centuries ago, to equate science and equations is unwise. And soon to be irrelevant, thanks to computing power. After all, equations are digital, and the universe is not.

        1. Equations are not digital, unless explicitly established to be discrete.

          Geometry is math. If your issue is simply with “equations” as a subset of “math” then fine. Without “quantitative math” you cannot say which concept is better at describing reality.

          You didn’t say ellipses were easy. You did say that they (or rather that correct concepts in general) should have somehow been deduced to be correct without resorting to precise mathematics to do so. You haven’t explained how this is possible without a-priori knowledge that they are correct. How was Kepler to figure out that ellipses were correct without math? The way he did it in reality was by building on the previous math and seeing where it lead.

          Novelty of the equations is irrelevant. It’s the fact that Special Relativity had rigorously defined math from which one could calculate consequences and compare them to reality which matters. Without that, there would have been no reason to believe the math-free concepts described had any relevance to reality.

          1. Anon: You put ideas in my mouth I would neither think, nor proffer. I did not say ellipses could have been easily figured out without equations (although it can be done!). I said the heliocentric theory was figured out at a time when equations were in the process of being figured out (thanks to Buridan, his students, and, in particular the “Oxford calculators”).

            Einstein’s contribution to Relativity was all about repackaging the concepts and the equations neatly. The Poincare’ group is hard to describe without “equations”.

            You are free to call Euclidean geometry “quantitative math”.

            Should I attract your attention to the contrast between “topology” and “combinatorial topology”? That could be cruel.

            By “digital” I alluded to the following. The incompleteness theorems of mathematical logic use the fundamentally discrete (“digital”) character of any mathematical expression, including equations, to demonstrate that no digital expression can capture all the expressions it can give rise to (one could say that metamathematics is NOT renormalizable…).

          2. Beautiful discussion,
            As the Universe is getting bigger (new space), the energy density from matter and radiation would be getting smaller, but vacuum energy density (cosmological constant) would remain the same.
            The entropy of almost every substance grows in proportion to the amount of substance that we have. Black holes only involve gravity. Towards event horizon mass-energy and entropy grows like the square. Quantum theory equations can calculate that – but the informations, fundamental for mathematics (equations) and quantum theory, Hawking’s formula for the temperature of a black hole, failed to find this entropy, because of too much mass thru equations.

            Every layman and expert feels earth is flat, without conceptualizing the “reality” of enormous spherical earth. But our day to day equations and mathematics not includes this “reality” everytime. Including this negligible frame of reference doesn’t make any difference.
            To make mathematics or equations work, we need axioms like particles or mass-energy invariance. Einstein repacked this layman understanding of flat earth (mass-energy invariance) by making speed of light “c” (enormous spherical earth) as reference frame.
            Why this same concept is not working with Gauge invariance equations up to vacuum-energy – leading to dicrepancies and failures of mathematics – because mass-energy and entropy grows like the
            square towards event horizon (>c), the entropy may start to decrease – where “c” as reference frame may no longer enormous ?

          3. I could not edit. I want only two words in block letters to show the above, does not mean, the particle nature (mass energy invariance) is a humbug of relativity. The wave nature (gauge invariance) represented by quantum field, contrasting with quanta, is more near to reality – but we can only have knowledge (Erkenntnis) of things in the phenomenal realm or of the conditions for the possibility of experience; things outside of space and time or beyond the bounds of sense—the “supersensible”—are off limits for our knowledge claims. In uncertainty, we have access, only to empirical certainty ?
            The supercomputing with informations may complicate the access to reality ?

          4. Patrice Ayme: I didn’t say you said it would be easy. You claimed I claimed that, twice now, apparently just so you could claim I was putting words in your mouth. But what I actually claimed you claimed is what you just claimed once again: that Kepler could have concluded that ellipses were a good model — as good or better than existing models — without actually comparing the output of that model quantitatively with the quantitative data he had on their positions using a calculation that involved at some point an “=” with a number on one side. So stop playing games and justify your claim.

            It isn’t cruel at all to bring up something that seems to clarify that it really is just algebra and it’s nefarious “=” that you’re upset about Matt implying is necessary for a good theory. It’s not cruel, but rather just annoying, that you don’t expound on how you think you can go about comparing theory to reality without quantitative measurements and a commensurate calculation from theory.

            It’d be nice if you’d also explain what kind of non-equation-based math you would expect to find in Hawking’s paper that would nullify Matt’s critique.

            It’d also be nice if you’d tie this together with your earlier point that “With the wrong concepts, it doesn’t matter how many equations one writes.” So, is non-quantitative math what you call “concepts” and “ideas”? Because to me non-algebraic math is just as precise as an equation. And again, you need to explain how you know that your “concepts” are right without an equation that lets you compare them to reality. Cart before horse is what it looks like to me.

  27. Here is another one, this time from Physics World, entitled: “Magnetic Monopoles Seen in the Lab”. This is what journalists do – when the news is slow – sensationalize.

    By the way, for me a ‘black hole’ is any object with an escape velocity > c. When anyone goes beyond that, with singularities, wormholes, gateways to other universes or unknown dimensions, etc. you lose me. Let me know when you get there…

  28. Professor Strassler,

    To what does your comment “on the contrary refer”?

    The Eot Wash group and others have used torsion balances to test the inverse square law inside massive bodies. These are regarded as STATIC measurements because the probe moves only a tiny distance compared to the size of the body.

    What has never been done is to observe the motion of a test object through the center. The results are assumed to be known only by extrapolation (about which, see below).

    Since this post is mostly about General Relativity, it is relevant to mention that the general relativistic counterpart for the standard Newtonian (harmonic oscillation) prediction for the result of Galileo’s experiment corresponds to a difference in clock rate. The INTERIOR Schwarzschild solution predicts that the rate of a clock at the center (r = 0) is a minimum. What is the physical cause of that? Schwarzschild’s interior solution has never been tested. Doing Galileo’s experiment would serve as a test.

    Everybody wins if we simply acknowledge that we have a gap in empirical evidence and make plans to fill it.

    Concerning the assumption that the result of the experiment can be claimed to be known by extrapolating from outside to inside matter, or from static measurements to direct observations of motion, please consider the advice of Herman Bondi:

    “It is a dangerous habit of the human mind to generalize and to extrapolate without noticing that it is doing so. The physicist should therefore attempt to counter this habit by unceasing vigilance in order to detect any such extrapolation. Most of the great advances in physics have been concerned with showing up the fallacy of such extrapolations, which were supposed to be so self-evident that they were not considered hypotheses. These extrapolations constitute a far greater danger to the progress of physics than so-called speculation.”

    1. Richard,

      Nice Bondi quote. Still true I think and no doubt always will be. Every now and then, nature smacks us in the head and says “you barely know me.” We are never humbled however. And the last time we really got smacked was only 16 years ago – we all ‘knew’ the universes expansion must be slowing, but when we actually got around to measuring it…Smack!

      So here we are in 2014 with our oh so serious arguments concerning the 5% of the universes energy we still think we ‘know’. Better duck…I sense another smack coming!

  29. No loss of information means, I guess, that the information remains but in a scrambled state? In other words if I had a brain the size of the Universe I could reassemble each particle into its original matter state? Just kidding, maybe.

    1. Basically no loss of information means that if you put different things in, you get different things out. (And can thus tell what went in… somehow.) With black holes however it seems possible to put different things in (if they have the same amount of energy.) and get the *same* thing out.

  30. I want to be clear. I like to see the scientific sausage made. I take extreme exception to “The average person on the street couldn’t care less and wants us to get our facts straight before throwing ideas around in the media.”

    Now I would like the media to do a MUCH better job than they do, which is why I read science blogs.

    As a lay person I’d like to understand why some are so bothered by the “loss of information”. Its not a loss of mass, or loss of energy, just a loss of information. Where did the idea for the conservation of information come from? And what proof is there that it is fact true?

    1. If quantum theory is true, then information cannot be lost. It’s fundamental to the mathematics of the theory.

      Therefore, if information is lost, quantum theory is false and must be extended to something else.

      Since the entire description of particle physics, and everything built upon particle physics, is based on quantum theory, the overthrow of quantum theory would be the most important event in fundamental physics since the invention of quantum theory.

      That means that the information paradox is among one of the most important problems in fundamental physics — because on it hinges the question of whether quantum theory must be replaced with something more general.

      1. In


        at slide 26, Polchinski lists three of the postulates of black hole complementarity, one of which cannot be true:

        Hawking radiation is in a pure state
        No drama is experienced by an infalling observer at the horizon
        Semiclassical gravity is a valid EFT outside the horizon

        It is an interesting problem.

        What’s more catastrophic (or exciting for theorists)? Introducing non-unitarity, accepting the possibility that one or more fields do not quantize (in a sufficiently strong gravitational field, or at all), or recognizing a failure of the equivalence principle or of gauge/gravity duality?

        Any of these outcomes would certainly be A Big Deal for particle physics, and there does not seem to be any consensus on which (if any) is most likely.

    2. So — in terms of seeing the sausage made, the right place to see that done is probably the blogs, because there the audience is more limited and self-selecting.

      I don’t have a problem with Nature magazine covering a story like this either, in principle, if they avoid the kind of headline that generates a problem.

      But when a story like this goes mainstream, it gets read not just by you but by lots and lots and lots of people who’ve never read a science blog and learned about black holes from some TV show, maybe the Big Bang Theory or more likely Star Trek. For those people, hearing that “Hawking Says There Are No Black Holes” is not a good thing, because, unlike you, they won’t delve.

      And the reason it’s really bad is that it plays into the anti-science folks’ hands. It makes it sound as though scientists change their minds every day about what seem like well-established facts, and undermines confidence in the scientific process.

    3. On any given day, one can probably find a pop-sci article about some major game changing scientific discovery, yet what has come of these discoveries we always hear about? Doctors can charge more and cell phones got bigger… what else? Consider recent attention for the black hole compliments and the fire hydrants. If that isn’t the physics community clearly saying, “We want to focus our small media lens on sausage-making,” I don’t know what is.

  31. I wonder what your justification is when you say the dictionary definition of the word ‘theory’ is not applicable in physics? To my knowledge, it has been a great benefit to the world physics community to use standard English.

    1. I’m quite surprised by your remark. The word “Force”, in physics, does not match the dictionary definition. The word “Energy”, in physics, does not match. Neither do “Mass”, “Momentum”, “Particle”, “Wave”, “Function”, “Field”, “Interaction”, “Light”, “Chaos”, “Mechanics”, “Scale”, and a host of others. And “Theory” most certainly doesn’t. In short, I believe your knowledge is incorrect.

      1. I am not at all surprised by your remark. The technical definition of force is mathematical and agrees perfectly with one of the definitions you will find next to ‘force’ in the dictionary. In fact, all those other words are applied in the most intuitive way as phonemes representing abstract mathematical ideas that transcend language. However, your defintion of theory directly contradicts the dictionary defintion and has no precise mathematical defintion other than the one you invented here. Perhaps we should invent our own new language so there isn’t confusion when we say the dictionary is wrong.

  32. Philosophically I believe that everything in this Universe that has a beginning must also have an end. How? I don’t know, but it will. Maybe not science, but it is nonetheless true.

    1. So you’re betting against the Second Law of thermodynamics then. Somehow I feel like I’ve seen this movie a few times before…

  33. So what do call a Black hole that isn’t? Maybe a dark gray hole, though I think it remains black. There is a large cloud of gas streaming towards our central Black hole. Is there a chance that information learned as the gas enters the event horizon help solve a little of the mystery?

  34. If one neglects speculations about “evaporation”– which idea arose when quantum theory was applied to “classical” black holes–then the thing described by general relativity when the equations become singular is less like a hole than it is like a point.

    I find it curious that so much attention should be given to such extraordinary exotic things when we have not yet empirically explored the gravitational consequences of ordinary holes through ordinary bodies of matter. Einstein’s, and even Newton’s, gravitational equations pertaining to motion inside matter have never been tested. Thus, the most ponderous half of the gravitational Universe has never been explored.

    Almost 400 years ago Galileo proposed dropping a cannonball into a hole through the center of Earth. Using the Earth as a source mass is obviously impossible. But by using smaller bodies, either in a modified Cavendish balance or in an orbiting satellite, the test is quite possible with modern technology.

    Since the whole idea would be to observe the behavior of two bodies of matter that are left to themselves in the simplest possible state, such that they do not collide, the apparatus needed to conduct the test may be called a Small Low-Energy Non-Collider.

    1. On the contrary, the precise studies of Newton’s law of gravitation using torsion balances take place inside of containers whose gravity is not irrelevant. http://www.npl.washington.edu/eotwash/

      In getting these experiments, which are extremely delicate, to test Newton’s laws, it is assumed that gravity involving the exterior of the container cancels inside the container exactly as Newton says it should at distances larger than the short distance which the experiment is intended to probe.

  35. Very interesting.

    What I think is:

    1. I am inclined to agree with Hawking philosophically, albeit for other reasons.
    2. Why Firewallparadox? The firewall idea is what one may expext logically from thermodynamical effects related to time-differences.
    3. Why Informationparadox? Information getting lost is what one may expect logically from entropy.
    4. I agree with Black Holes having an endless number of shades of black.

    1. The problem is that entropy is what you have when you have incomplete information. In quantum mechanics, if you knew everything about the initial conditions for a physical process, the entropy would always be zero. The information paradox is that even in this situation, there seems to be a loss of information if you study quantum mechanics involving a black hole.

      Suppose you take a known initial condition (entropy = 0) with some material in it, allow the material to collapse and form a black hole (apparently with entropy, yet the true entropy should still be zero) and then allow it to evaporate (still entropy = 0, if quantum mechanics is true). No one knows precisely how the entropy can remain zero (without destroying the interior of the black hole) but if it doesn’t, then quantum mechanics is wrong in the presence of a black hole. That’s what Hawking used to think, in fact. But then developments in string theory (“AdS/CFT correspondence”, which allows you to see that the process I just described can in fact occur in quantum mechanics) showed quantum mechanics isn’t wrong in this situation… Hence the crisp paradox.

      1. For the entanglement of same material, the entropy toggles between increase and decrease. Only one is accessible for the observer outside the event horizon as firewall or black hole complementarity. So in complementarity sense, there is no black hole. Even there is something interior, it is beyond the bounds of sense – due to information scramble ?

      2. Thank you very much for your explanation.
        I can’t imagine 0 entropy. Pascal said “To be completely still is to be dead”. Heraclitus said “Panta rhei, ouden menei”. Moreover I would not know how to determine the exact time of any 0 entropy moment. To me a 0 entropy state would only be possible in a 0 time state. That I can’t comprehend.

  36. Matt: as darkmatterdarkenergy suggested above, I think Hawking was being deliberately provocative here. And as Peter Woit more or less said, Hawking knew what he was doing. He knows how to hype. He knows how to work the media. He gave them a soundbite that he knew would make headlines. So I’d keep your skin out of this game if I were you. Especially since gravitational time dilation at the event horizon is said to be total. So how long does it take for one quantum fluctuation to happen? Answer: forever.

    1. There you make a mistake. Your statement “gravitational time dilation at the event horizon is said to be total” applies to classical, unchanging black holes. For a quantum black hole that is created and then evaporates away, your statement is false. You can’t get away from this problem so easily.

      I don’t think Hawking *did* know what he was doing. I think he thought he did.

      1. Hi Matt: My impression is that even a quantum black hole (of astronomical size) may take billions and billions of years to evaporate. Is that wrong?

        1. That’s clearly true, since the one at the center of our galaxy has apparently been around for billions of years without evaporating. But it has probably had plenty of food, so maybe that isn’t quite the example you’re looking for.

        2. Hawking Radiation power is inversely proportional to the mass squared, and for a solar mass black hole is around 10^-29 W. Clearly it’s going to take something with the mass of the sun a long time to evaporate at that rate. The evaporation time is proportional to the inverse of mass cubed, so Sag A* which is a pretty small SMBH at mere millions of solar masses, is going to be around a long, long, LONG time.

          And that’s assuming no source of energy influx. Currently a solar mass black hole is absorbing more energy from the Cosmic Microwave Background than it loses to Hawking Radiation. So this process won’t really even begin to start until the CMBR is red-shifted to nothingness.

          1. Wow! That’s really very interesting! I didn’t realize that about the inverse square and the microwave background. Thanks for that mini-analysis, whoever you are.

      2. I really don’t think I made a mistake Matt. IMHO the key to it is to imagine you’re holding a laser pointer up vertically. Now gradually increase the mass of the planet you’re on until it’s a black hole, then ask yourself why the light doesn’t get out. It doesn’t curve round. It doesn’t slow down. It doesn’t fall back. We have evidence for black holes. But we don’t have evidence for Hawking radiation. If you catch my drift.

        1. Have you actually done the calculations of the geodesic as the mass of the planet increases? Or is this just taking place in your imagination?

  37. Are Einstein’s field equations 100% correct. I am thinking of a seven letter name that begins with “M” and ends with “m”, in the Latin alphabet at least.

  38. I don’t see why you’re so upset at the press here. Hawking writes a paper explicitly saying “there are no black holes”, in the sense of no event horizons beyond which light cannot escape. Given his practical typesetting difficulties, his paper is not especially different in terms of use of precise mathematics than those of other people working on the same subject. A large group of the most prominent people in the subject are doing similar kinds of work, saying things about it like “This is a 9 on the Richter earthquake scale—it’s by far the most shocking and surprising thing that has happened in my career.”

    Given all this, what is a competent journalist going to do: write an article like the one you link to, or decide that there’s a lot of ill-defined hype going on here, best to not inflict this on the public? I’d certainly argue for the second course of action, but if a journalist decides to go with the first one, I don’t think it’s the journalist who is to blame, but the physicists involved.

    1. Well, in my judgment the media has created the impression that Hawking is saying that there are no black hole-like objects, not that the black-hole-like objects aren’t quite black. And I verified this by checking with non-expert friends as to what their impression was.

      This creates a strong level of confusion in the public that will take years to undo. For years I am sure I will give talks in which I will mention the black hole at the center of the Milky Way and be asked “but didn’t Hawking say those things don’t exist?”

      It would have been better to say “Hawking says black holes aren’t quite black” or “Black holes might be grey”, and it was a huge error to write “Hawking says there are no black holes”. You and I understand that (roughly) he means not “There are no black holes“, but rather “There are no black holes”. But how can a non-expert know, if further explanation is not provided? The fact that Hawking’s statement has zero implications for the *astrophysics* of black holes (which is where most non-experts encounter the concept) is nowhere mentioned in most articles. For a gravity or quantum theorist worried about issues of principle, this is a very big issue, but for any normal person with other interests, Hawking’s paper is about counting angels on pinheads, or vice versa. [We’re all too self-important in this field, in my view.]

      I completely agree, of course, that Hawking is not alone in writing vague papers about the black hole paradox, with few if any equations that can be used to obtain reliable conclusions. (Indeed I said so a while back, as you may have read: http://profmattstrassler.com/2013/09/16/a-quantum-gravity-cosmology-conference/ ; so did Polchinski, very prominently, in his opening talk at that conference.) The black hole paradox is proving to be an extremely hard problem. I have never heard my black-hole-expert colleagues so humble as in the last three years; twenty years of work since the idea of complementarity, and not that much to show for it. And a proposal, by Hawking or anyone else, for a solution that does not contain the mathematics to back it up is not worth very much; we’ve seen plenty of those, and still the problem is unsolved.

      Indeed, after Hawking’s talk that this paper was based on, Susskind’s response was that he agreed with this line of thinking, but that the real problem is that someone has to show exactly where the argument of Almheiri, Marolf, Polchinski and Sully (who pointed out the flaw in complementarity, and launched the “firewall” debate) goes wrong. This Hawking has not done, nor has anyone else. Without a demonstration of a precise flaw in their logic, or a precise demonstration in favor of his own logic, Hawking’s ideas are no better off than anyone else’s… and it’s simply the media’s “grand old man” obsession which makes them report on his papers more than on those by a bright young unknown person who’s actually more likely to solve the problem. That’s a situation which does the public, and science, no good.

  39. Amazing … at the center of every black hole is an unscrupulous science journalist. I like it. (I’ll do the math for second authorship.)

  40. At least if Hawking’s theorem are generally accepted by his peers and singularities are shown not to be found in black holes mathematically. We could stop all the needless speculations about wormholes, warp engines, baby universes, etc and other whats not.

    However, the most loved big bang cosmology will require a re-look as well since the universe did not start from a single point of infinite density but from a minimum volume of a fixed energy-mass.

  41. Matt, I appreciate when you try to set the media straight on these matters, but I think, for the most part, neither the media, nor indeed their readers, pay much attention to your well-reasoned posts, they like the snappy headlines!

  42. Us lay people do care beyond the normal media link and explanation as news articles, so I appreciate you as a group of scientist helping toward clarity in this regard. So thanks.

      1. Hmm… I don’t like this definition at all. It seems wrong on many counts. For one thing, it has nothing to do with the object’s mass. It has to do with how compact it is relative to its mass, and thus, how strong its gravity becomes. For instance, the sun could be a black hole, if you squeezed it enough. Even you could be a black hole; a very small and short-lived one, but… something you can aspire to.

        1. Then could you demonstrate qualitatively how the black hole in it’s simplest form as an equation. What you then feel comfortable with. I am always seeking this foundation as scientists explain the most fundamental example, so as to contrast what this article is saying from that basis?

  43. Sabine Hossenfelder has a slightly different take from yours. She doesn’t think there is anything controversial or remarkable about Hawking’s guess: “That is an opinion which is shared by many of his colleagues (including me) and there is nothing new about this idea whatsoever.”

    She also emphasizes that “dark holes” (my term; she calls them “apparent black holes”) are currently indistinguishable from black holes empirically.


    1. I have no skin in this game, but I suppose Sabine is probably a bit annoyed since she has the same point of view that is being attributed to Hawking. She’s right that Hawking isn’t alone; indeed right after Hawking’s talk, Susskind’s comment was “we’re on the same team this time”, or something like that. [This is in reference to how Susskind and Hawking were on opposite “teams” in the 90s.]

      But Hawking makes some specific points that aren’t in the media but have some scientific interest; I’m not expert enough to know which ones are new.

  44. Nice post.Yes, scientists have to be very careful with their words these days just like lawyers! Anyway, I understand , the event horizon is precisely the place where space and time coordinates are in the process of getting switched into each other. So it may be quite intriguing to say that the apparent singularity would disappear as a function of time. Also isn’t singularity at r=0 a big crushing problem which defines black holes? What does Hawking say about it?

    1. Your definition of the event horizon works if the black hole is unchanging with time. The definition of horizons is very much more complicated even for a classical black hole that changes with time, and much worse in the quantum context where we don’t have good definitions.

      For Hawking’s proposal to make sense, I believe there could be no singularities associated with black holes. Of course that would not be surprising; the singularities probably represent a breakdown of Einstein’s theory of gravity and the need for something that goes beyond it, so it’s very commonly suggested that the singularities we see in classical gravity will be absent in whatever theory generalizes it. So that’s not the radical part. The radical part is to suggest that, from the point of view of someone falling into the black hole, everything that falls into a black hole WILL get out eventually, though highly scrambled.

  45. Thanks for the text! I knew I had too much sensationalism in this statement, but could not explain why.

  46. hi i got Q what happen if BH be bigger inside than outside if that be help or not? im not expert but i think (maybe wrong) that be solution for most of trouble with BH including singularity he newer be create in this case becouse density inside BH newer be enough big this same happen with information or maybe not??

    1. No, the interior volume of the black hole does not help. The problem is that once the black hole has evaporated, it’s gone from the exterior point of view, so it doesn’t matter what its interior volume was. Once it’s gone, the question remains: is the information about how the black hole formed encoded in the radiation it emitted as it evaporated, or not? And if so, how could that information be put into the radiation while still allowing an observer who is falling into the black hole to see and move around in the black hole interior?

      1. I think no. Mixed quantum state (statistical ensemble) not accessible ?Physics came from philosophy.

        According to Immanuel Kant, we can only have knowledge (Erkenntnis) of things in the phenomenal realm or of the conditions for the possibility of experience; things outside of space and time or beyond the bounds of sense—the “supersensible”—are off limits for our knowledge claims.

  47. Thanks for writing this post. The media frenzy was driving me nuts! Obviously Hawking was being provocative to other black hole researchers and the physics community, but the media have no ability to understand the subtleties. And they are trying to “sell newspapers” after all,

  48. Dear Matt, I think that Hawking’s proposal is a bit more radical than what you present.

    At any rate, a black hole is *defined* by its having an event horizon, a boundary of no-escape (see e.g. the first sentence in Wikipedia), so saying that even these objects don’t have event horizon *is* equivalent to saying that black holes don’t exist.

    Of course that the information gets out etc. so the event horizons are not that “strict” but the normal expectation about the validity of the classical limit implies that whenever it makes sense to (approximately) describe the phenomena as taking place in a classical geometric background, the phenomena respect the causal restrictions of a classical geometry with an event horizon.

    I feel that you are trying to argue that “of course famous physicists like Hawking couldn’t say a thing that other physicists consider totally silly” except that I think that this is what is actually happening.

    1. Hi Lubos. I think the mismatch here is between what the public understands about black holes versus what experts understand about black holes.

      For an expert, Hawking’s proposal is radical in some ways. It’s also probably wrong in some ways, maybe in all ways. You and I care a lot. The average person on the street couldn’t care less and wants us to get our facts straight before throwing ideas around in the media.

      What the average person understands, quite naturally, about black holes is that these are places that if you and your rocket ship fall in, you can’t get out. That’s still true in Hawking’s proposal. *You* can’t get out. To you and me, the notion that the information about who you are is still encoded in subtle quantum correlations among elementary particles, and *those* things really can get out, is radical (though not unprecendented) and interesting. To an average person, it’s completely irrelevant.

      The media reports tend to suggest that “the objects currently called black holes” don’t exist, not that “black holes aren’t actually black”, which is what they should say. They tend to imply that you and your rocket ship could in fact get out… obviously false.

      So the problem is that while I agree Hawking’s proposal is radical for a quantum gravity physicist, it’s not radical for an ordinary person; there are still objects at the centers of galaxies that we can safely call black holes, and big collapsing stars still form them. The technical fact that they might not be black, and instead just really really dark for a really really long time, is not of interest to anyone who isn’t trying to solve the problems of quantum gravity. And so the media should not be reporting, blindly, that black holes don’t exist.

      As to whether Hawking’s proposal is silly, I’ve heard so many wrong proposals about this problem from so many smart people that I have zero confidence in my ability to judge, especially since I am not working on this problem myself.

      1. Dear Matt, thanks for your reply. I agree that lots of silly things have been written in that field, and so on. This is not an issue. For me, Hawking is still a hero, despite these things.

        By the way, he may have some trouble to write TeX (think how it could be done if you shared his body’s restrictions) so I will tend to read his papers even without dollar-delimited equations, especially because I know that he used to be able to calculate path integrals in his head, so I don’t think that your criticism of the absence of equations is too legitimate. It’s still plausible he can sort out all the key things in his head, using equations, and produce the output in a verbal form.

        I don’t think that the laymen imagine the definition of the black hole as a place from which just people can’t escape. Even if you fall into the Sun, you won’t escape. You will be burned. You can’t even escape from the Earth’s gravitational field – even Olympic sprinters usually fail to reach 11 km/s, the escape speed from Earth. 😉 The problem is that you won’t even be able to send radio signals informing others about your last moment. So in my opinion, even the laymen understand that the light’s ability to escape is what matters. I think that the educated laymen – good readers of popular books – do understand that this is why the black holes are called black: they are black because *light* cannot escape.

        Hawking has explicitly written that the light can escape. Hawking is apparently revising a lot because he has also called his work in the 1970s as the “greatest blunder”. It’s hard to get the exact quote – whether he meant all of his papers or just the suggestion that the information is irreversibly lost. I feel it is the former because he wouldn’t use such strong words if it were the latter.

        According to my reading of the new paper, he is really bothered by the time-reversal asymmetry of the BH diagrams – the formation looks different than the evaporation – and he believes that this asymmetry is a contradiction (with the CPT theorem) which is why he rules out the usual Penrose diagrams of the formed and evaporating black hole even as an approximation. There are several other reasons to think that this is what he wants to say.

        In that case, he’s wrong because the time-reversed (or CPT conjugated) processes are still possible. One may draw the Penrose diagrams (of a star collapse followed by the evaporation of a BH) upside down. Just these processes correspond to decreasing entropy and like all decreasing-entropy processes, they’re exponentially unlikely to occur in the real world.

        The event horizons do exist to the same extent to which geometry exists. It is an approximation but as long as we talk about the spacetime geometry at all, we must also admit that this geometry has event horizons (in the same approximation in which the geometry exists). Saying otherwise is a full-fledged denial of general relativity. Quantum gravity, when done properly, doesn’t really deny classical general relativity.

        1. Hi Lubos – thanks for your reply. I agree that the absence of equations in a paper by Hawking is not a demonstration there’s no math behind it — but he doesn’t work alone, and if there were equations of real content, he could certainly write a paper with an assistant or collaborator, as he has done many times. Moreover, in this case, a mathematical demonstration IS required, because the whole firewall discussion, and indeed most of the discussion about the information paradox for the last 30 years, has suffered from the absence of real calculations. Certainly there’s nothing you or I would call a “theory” in Hawking’s paper, explicit or implicit.

          I disagree with your point of view about public perceptions, but agree with your criticism of the way I expressed it in my previous reply. I should have said: “the notion is that if you and your rocket ship fall in, you and your rocket ship will not be able to get out, no matter how powerful is your rocket ship.” And even if I accept your suggestion that a typical layperson thinks about the radio signals you can’t send to your friends outside — well, even in Hawking’s proposal, you still can’t send those radio signals, because they’ll get completely scrambled. So I still think that for the average person there’s no real change… yet. Especially since there’s no math here.

          I haven’t thought about Hawking’s paper long enough or carefully enough to judge your interpretation and critique, but thank you for providing it. Hawking would not be the first person to judge his own early work harshly, and possibly unfairly, and possibly incorrectly. There *is* something wrong with his calculation, but we knew that already, and it’s not because it’s a blunder; if it were just a straightforward blunder, we’ve had 40 years to find the error. Frankly, Hawking’s recent paper sounds like most of the other suggestions I’ve been hearing in the firewall context: desperate words not backed up by brilliant insights and crisp equations. Not that I have anything useful to add to the science. I suspect we should be looking among our postdocs and graduate students for the solution, not our senior faculty.

          1. Dear Matt, I am sure we would largely agree about the amount of maths one may reasonably expect in a paper that really moves serious science to a higher level, and even about the expectations whether some old chaps or postdocs or graduate students are doing the most careful and original and promising work in this subfield – yes, it’s largely the latter, although I wouldn’t view this age stereotype as a dogma, either.

            There are also other things we might disagree about; you may also look at a new text of mine,


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