7 ms·

Mathematicians Disprove Conjecture Made to Save Black Holes

227 points by bainsfather 8y ago

nerdponx 8y ago
Their work is subtle — a refutation of Penrose’s original statement of the strong cosmic censorship conjecture, but not a complete denial of its spirit. I wish somebody out there could cover social science research and politics with this kind of attitude. This is really good science writing.
- labster 8y ago
  Einstein and Penrose theory totally crushed by mathematicians -- that makes a better headline.
  - nerdponx 8y ago
    "Einstein and Penrose were wrong; this is why"
    - philipov 8y ago
      "10 crushing proofs Einstein and Penrose don't want you to know" : Best headline.
      - diegoperini 8y ago
        What color is this proof: Einstein or Penrose?
bencollier49 8y ago
So spacetime exists beyond the Cauchy horizon, but it's discontinuous? What on earth would discontinuous spacetime involve? It sounds like a sort of shattered chaos of torn-up bits of space.
- nerdponx 8y ago
  It's not discontinuous, its derivative (a function describing the rate of change of space time) is apparently discontinuous, or infinite, or something else equally hard to picture. Plenty of strange things can happen with derivatives, e.g. https://en.m.wikipedia.org/wiki/Cantor_function https://en.m.wikipedia.org/wiki/Cantor_function
  - jordigh 8y ago
    I don't find failing to be differentiable all that strange, even if the failure is on a perfect nowhere dense set. What I find weird is that the derivative, if it exists, cannot have a jump discontinuity. That means that the only other kind of discontinuity it can have is infinite oscillation like sin(1/x) near zero. This one is a bit of an obscure property of derivatives, corollary to theorem 5.12 in Baby Rudin.
    - jerf 8y ago
      "What I find weird is that the derivative, if it exists, cannot have a jump discontinuity." You mean the derivative of a specific function you have in mind, like perhaps the field equations? Or do you mean something other than what I understand by a jump discontinuity in a derivative, such as one gets for f(x) = {-x for x<0, x for x>=0}? Tone: Clarification request for my own understanding, not a "gotcha" post; I strongly believe you are saying something true but there's just too many details elided because they are trivial to you for me to quite follow, and I'm intrigued enough to want to be able to follow up, if you'd be so kind as to indulge me.
      - qubex 8y ago
        What s/he is saying, if I understand correctly, is that two and only two kinds of discontinuities in derivatives (and second- and higher-order derivatives) can exist: jump derivatives and those exemplified by the pathology inherent in sin(1/x) at the origin thereof; given that spacetime continues beyond the Cauchy horizon but the derivative does not, the first kind (the abrupt ”vertical step” kind) must be ruled out, leaving only the second variety as a candidate. Graph that function, and it’s first and second derivatives around the origin, and you will begin to realise how bizarre this behaviour is and what strange implications it may have. (Then again, this is deep within a black hole, in an area where time and the radial dimension of space are switched, so it’s just a new kind of devilry in an already fraught area.)
stevespang 8y ago
Touche Einstein. God DOES play dice with the universe beyond the Cauchy horizon
deleted 8y ago
[deleted]
namibj 8y ago
Uh, this is why I tried to study pure maths (it's less physics and more weird differential geometry) I can recommend this paper [0] that talks about simulations that show a black hole just implodes in a weird way and kind of does not stop imploding, due to space-time getting stretched with a speed above that of light, as measured within a frozen moment in time, and summed over some line from inside to outside. A working analogy could be a 2d-spacetime, represented in 3d-space as a soap bubble film. Imagine the traditional visual funnel shape the space time around a black hole is often depicted as, compared to the downwards bump normal stars/planets are depicted. So, now, the thing is that the effect of gravity, e.g. gravitational waves, are bound by the speed of light. They can not escape a black hole. In the soap example the gravity waves would be film thickness waves, e.g. longitudinal waves in the thin soap sheet. Those are bound by the speed of sound in their medium. Imagine a stream of air with significantly higher speed than the sound in the soap, getting blown downwards this funnel. Also imagine the funnnel still having a closed tip made from soap at the start. Thing is, this air will hit the tip, propell it downards, and suck the part close to the center down just by itself, without the center indirectly pulling on it. Due to the supersonic nature, the ripple created from the initial impact of air onto the center will _never_ get out of there, just because the medium the waves travel through, when measured over the distance from where the wave is right now, to where the outside world with neglegible space-time (or soap-film) curvature is, expands faster than the wave travels. This does not mean the wave does not travel at all, just that once the distance you want it to travel increases enough, the propagation medium's expansion results in weird effects. If someone is willing/able to point me to some research or possibly even wants to use existing skills with the related differential geometry maths, I'd really like that. Edit: I might add that anything that falls into the black hole will, even in it's own reference frame, _never_ reach the center, and the only reference frame that possibly sees a steady state field curvature in finite local time could be the center of the collapse. [0]: https://arxiv.org/abs/1402.1524 https://arxiv.org/abs/1402.1524 (Which was published about half a year after I initially and timestamped communicated the idea to a physics teacher who was willing to explain me the differential maths used in Einstein's field equations.)
- JadeNB 8y ago
  > https://arxiv.org/abs/1402.1524 https://arxiv.org/abs/1402.1524 (Which was published about half a year after I initially and timestamped communicated the idea to a physics teacher who was willing to explain me the differential maths used in Einstein's field equations.) Maybe I'm misunderstanding your point, but your parenthesis seems to suggest that you would like to claim some credit for the idea. If not, then you can just ignore what I'm about to say. If so, then your comment seems to suggest that you came up with the idea, but weren't sure about the mathematics of it. In modern physics of this type, where experimentation is not practical, the math is the physics; that is, I think the problem is not so much coming up with ideas—my impression is that there are hypotheses and to spare—but rather being able to back up those ideas with rigorous calculations.
nyc111 8y ago
> In classical physics, the universe is predictable: If you know the laws that govern a physical system and you know initial state, you should be able to track its evolution indefinitely far into the future. ... [According to physicist Demetrios Christodoulou:] "This is the basic principle of all classical physics going back to Newtonian mechanics. You can determine evolution from initial data." This is a famous mantra repeated by physicists but it is not correct. Newtonian physics cannot even predict the future positions of three body from their initial positions. And Newton knew and stated that his doctrines could not predict planetary orbits in long term and he invoked the very scientific and physical notion (or maybe footballers term) of Hand of God. Thus, Newton claimed his doctrine could not make accurate prediction not because they were wrong but because God erred to create the universe according to Newton’s doctrines. Consequently, according to Newton, God once in a while nudged the orbits to make them move correctly according to Newtonian doctrines. According to Newton himself initial states cannot predict long term behavior. So how come NASA can predict so accurately planetary motions by using the so-called Newtonian Mechanics? The answer is easy: by not using Newtonian mechanics. NASA uses sophisticated mathematical methods or numerical integration to calculate orbits. But since they use as a unit conversion factor the strategically named Newton's Constant of Gravitation as one of their mathematical terms they feel they are justified to declare that they use Newtonian mechanics to compute orbits. So what happened is that at some point, maybe in the 18th century this philosophical -not physical- assumption entered the physics literature and gained the status of truth after centuries’ of repetition. But if we question the mantra we see that the so-called classical theories do not claim that they can predict future states by the initial state. Phycists do.
- jonathanyc 8y ago
  What on earth? Not having a closed form for something is decidedly not the same as not being able to use it to predict anything. That’s like saying so-called computer programmers can’t actually predict anything about their programs will do.
  - masteranza 8y ago
    Do not bother this guy. Apparently he is either crazy or ignorant. The solar system is stable in the sense of time periods necessary to make NASA their calculations and the Lyapunov are small - all that's needed can be deduced from either Newton or Einstein theories.
jryan49 8y ago
Is this just another implication that general relativity is incomplete? We already know it must not be because it does not work at the quantum level.
- Florin_Andrei 8y ago
  Anything that has singularities coming out of general relativity is pretty much guaranteed to be incomplete. But we can ge close to some workable solutions in particular cases.
habitue 8y ago
Ok, yes, this is how you promote scientific research to a lay audience: 1) They don't bury the lede. The first paragraph says what the result is immediately, if you understand it already, you're done reading. 2) Inverted pyramid structure. After they explain what happened, they break apart the historical context of the problem itself and give copious examples and metaphors to give the gist of what the problem is about and why it matters that it was solved. I can't tell you how many of these popsci articles start out with "When Mary was a 3 year old, she used to look up at the stars and ... blah blah ... Now, she's taking on the scientific establishment and daring to do the unthinkable..." etc etc. I just dread skimming through the fluff to try to pick out what the hell was actually done. Thank you Kevin Hartnett (the author of this piece) for not attempting to turn scientific papers into a human interest story.
- snowwrestler 8y ago
  They're just different types of articles--straight news reporting vs feature writing. It's fine of course to not like one or the other style, but they are both effective ways of connecting with audiences.
  - davesque 8y ago
    It depends on the audience though. In this case, I think it's correct to say there's a strong chance that the reader is not interested in prose. The sad thing about the human interest style is that, if that's not what I'm reading for, I begin skimming as soon as I detect it and much of the author's work ends up being for nothing.
  - Florin_Andrei 8y ago
    Yeah, plain info versus story. Both have their uses.
- jblow 8y ago
  Amen. I am so tired of trying to read these articles that spend so much time on random personal backstories because they don’t have faith that the core subject matter is interesting to read. The worst are the ones that jump back and forth between A/B/C plots, jumping away before any satisfying conclusion is reached on any of them, as a way of tricking your brain into reading the article ... like a really bad TV show, or Westworld. All those articles can go burn in a hot, hot fire.
jniedrauer 8y ago
The non-deterministic nature of atomic decay by itself makes the universe unpredictable. And this is a thing that happens at STP. I think the author of this article might have forgotten that. There was never really any determinism to "save".
- computerfriend 8y ago
  General relativity is classical, so there is plenty of determinism to save.
8bitsrule 8y ago
As I recall, Gen. Rel. continues to explain all directly observable phenomena within limits of resolution. That's damn powerful. As for 'black holes', well ... believe what you choose. A prof. once told me that Einstein 'wasted 30 years' looking for unified theory. By that standard, so did Hawking I guess.

227 points by bainsfather 8y ago

Their work is subtle — a refutation of Penrose’s original statement of the strong cosmic censorship conjecture, but not a complete denial of its spirit. I wish somebody out there could cover social science research and politics with this kind of attitude. This is really good science writing.

labster 8y ago
Einstein and Penrose theory totally crushed by mathematicians -- that makes a better headline.
- nerdponx 8y ago
  "Einstein and Penrose were wrong; this is why"
  - philipov 8y ago
    "10 crushing proofs Einstein and Penrose don't want you to know" : Best headline.
    - diegoperini 8y ago
      What color is this proof: Einstein or Penrose?

bencollier49 8y ago

So spacetime exists beyond the Cauchy horizon, but it's discontinuous? What on earth would discontinuous spacetime involve? It sounds like a sort of shattered chaos of torn-up bits of space.

nerdponx 8y ago
It's not discontinuous, its derivative (a function describing the rate of change of space time) is apparently discontinuous, or infinite, or something else equally hard to picture. Plenty of strange things can happen with derivatives, e.g. https://en.m.wikipedia.org/wiki/Cantor_function https://en.m.wikipedia.org/wiki/Cantor_function
- jordigh 8y ago
  I don't find failing to be differentiable all that strange, even if the failure is on a perfect nowhere dense set. What I find weird is that the derivative, if it exists, cannot have a jump discontinuity. That means that the only other kind of discontinuity it can have is infinite oscillation like sin(1/x) near zero. This one is a bit of an obscure property of derivatives, corollary to theorem 5.12 in Baby Rudin.
  - jerf 8y ago
    "What I find weird is that the derivative, if it exists, cannot have a jump discontinuity." You mean the derivative of a specific function you have in mind, like perhaps the field equations? Or do you mean something other than what I understand by a jump discontinuity in a derivative, such as one gets for f(x) = {-x for x<0, x for x>=0}? Tone: Clarification request for my own understanding, not a "gotcha" post; I strongly believe you are saying something true but there's just too many details elided because they are trivial to you for me to quite follow, and I'm intrigued enough to want to be able to follow up, if you'd be so kind as to indulge me.
    - qubex 8y ago
      What s/he is saying, if I understand correctly, is that two and only two kinds of discontinuities in derivatives (and second- and higher-order derivatives) can exist: jump derivatives and those exemplified by the pathology inherent in sin(1/x) at the origin thereof; given that spacetime continues beyond the Cauchy horizon but the derivative does not, the first kind (the abrupt ”vertical step” kind) must be ruled out, leaving only the second variety as a candidate. Graph that function, and it’s first and second derivatives around the origin, and you will begin to realise how bizarre this behaviour is and what strange implications it may have. (Then again, this is deep within a black hole, in an area where time and the radial dimension of space are switched, so it’s just a new kind of devilry in an already fraught area.)

stevespang 8y ago

Touche Einstein. God DOES play dice with the universe beyond the Cauchy horizon

deleted 8y ago

[deleted]

namibj 8y ago

Uh, this is why I tried to study pure maths (it's less physics and more weird differential geometry) I can recommend this paper [0] that talks about simulations that show a black hole just implodes in a weird way and kind of does not stop imploding, due to space-time getting stretched with a speed above that of light, as measured within a frozen moment in time, and summed over some line from inside to outside. A working analogy could be a 2d-spacetime, represented in 3d-space as a soap bubble film. Imagine the traditional visual funnel shape the space time around a black hole is often depicted as, compared to the downwards bump normal stars/planets are depicted. So, now, the thing is that the effect of gravity, e.g. gravitational waves, are bound by the speed of light. They can not escape a black hole. In the soap example the gravity waves would be film thickness waves, e.g. longitudinal waves in the thin soap sheet. Those are bound by the speed of sound in their medium. Imagine a stream of air with significantly higher speed than the sound in the soap, getting blown downwards this funnel. Also imagine the funnnel still having a closed tip made from soap at the start. Thing is, this air will hit the tip, propell it downards, and suck the part close to the center down just by itself, without the center indirectly pulling on it. Due to the supersonic nature, the ripple created from the initial impact of air onto the center will _never_ get out of there, just because the medium the waves travel through, when measured over the distance from where the wave is right now, to where the outside world with neglegible space-time (or soap-film) curvature is, expands faster than the wave travels. This does not mean the wave does not travel at all, just that once the distance you want it to travel increases enough, the propagation medium's expansion results in weird effects. If someone is willing/able to point me to some research or possibly even wants to use existing skills with the related differential geometry maths, I'd really like that. Edit: I might add that anything that falls into the black hole will, even in it's own reference frame, _never_ reach the center, and the only reference frame that possibly sees a steady state field curvature in finite local time could be the center of the collapse. [0]: https://arxiv.org/abs/1402.1524 https://arxiv.org/abs/1402.1524 (Which was published about half a year after I initially and timestamped communicated the idea to a physics teacher who was willing to explain me the differential maths used in Einstein's field equations.)

JadeNB 8y ago
> https://arxiv.org/abs/1402.1524 https://arxiv.org/abs/1402.1524 (Which was published about half a year after I initially and timestamped communicated the idea to a physics teacher who was willing to explain me the differential maths used in Einstein's field equations.) Maybe I'm misunderstanding your point, but your parenthesis seems to suggest that you would like to claim some credit for the idea. If not, then you can just ignore what I'm about to say. If so, then your comment seems to suggest that you came up with the idea, but weren't sure about the mathematics of it. In modern physics of this type, where experimentation is not practical, the math is the physics; that is, I think the problem is not so much coming up with ideas—my impression is that there are hypotheses and to spare—but rather being able to back up those ideas with rigorous calculations.

nyc111 8y ago

> In classical physics, the universe is predictable: If you know the laws that govern a physical system and you know initial state, you should be able to track its evolution indefinitely far into the future. ... [According to physicist Demetrios Christodoulou:] "This is the basic principle of all classical physics going back to Newtonian mechanics. You can determine evolution from initial data." This is a famous mantra repeated by physicists but it is not correct. Newtonian physics cannot even predict the future positions of three body from their initial positions. And Newton knew and stated that his doctrines could not predict planetary orbits in long term and he invoked the very scientific and physical notion (or maybe footballers term) of Hand of God. Thus, Newton claimed his doctrine could not make accurate prediction not because they were wrong but because God erred to create the universe according to Newton’s doctrines. Consequently, according to Newton, God once in a while nudged the orbits to make them move correctly according to Newtonian doctrines. According to Newton himself initial states cannot predict long term behavior. So how come NASA can predict so accurately planetary motions by using the so-called Newtonian Mechanics? The answer is easy: by not using Newtonian mechanics. NASA uses sophisticated mathematical methods or numerical integration to calculate orbits. But since they use as a unit conversion factor the strategically named Newton's Constant of Gravitation as one of their mathematical terms they feel they are justified to declare that they use Newtonian mechanics to compute orbits. So what happened is that at some point, maybe in the 18th century this philosophical -not physical- assumption entered the physics literature and gained the status of truth after centuries’ of repetition. But if we question the mantra we see that the so-called classical theories do not claim that they can predict future states by the initial state. Phycists do.

jonathanyc 8y ago
What on earth? Not having a closed form for something is decidedly not the same as not being able to use it to predict anything. That’s like saying so-called computer programmers can’t actually predict anything about their programs will do.
- masteranza 8y ago
  Do not bother this guy. Apparently he is either crazy or ignorant. The solar system is stable in the sense of time periods necessary to make NASA their calculations and the Lyapunov are small - all that's needed can be deduced from either Newton or Einstein theories.

jryan49 8y ago

Is this just another implication that general relativity is incomplete? We already know it must not be because it does not work at the quantum level.

Florin_Andrei 8y ago
Anything that has singularities coming out of general relativity is pretty much guaranteed to be incomplete. But we can ge close to some workable solutions in particular cases.

habitue 8y ago

Ok, yes, this is how you promote scientific research to a lay audience: 1) They don't bury the lede. The first paragraph says what the result is immediately, if you understand it already, you're done reading. 2) Inverted pyramid structure. After they explain what happened, they break apart the historical context of the problem itself and give copious examples and metaphors to give the gist of what the problem is about and why it matters that it was solved. I can't tell you how many of these popsci articles start out with "When Mary was a 3 year old, she used to look up at the stars and ... blah blah ... Now, she's taking on the scientific establishment and daring to do the unthinkable..." etc etc. I just dread skimming through the fluff to try to pick out what the hell was actually done. Thank you Kevin Hartnett (the author of this piece) for not attempting to turn scientific papers into a human interest story.

snowwrestler 8y ago
They're just different types of articles--straight news reporting vs feature writing. It's fine of course to not like one or the other style, but they are both effective ways of connecting with audiences.
- davesque 8y ago
  It depends on the audience though. In this case, I think it's correct to say there's a strong chance that the reader is not interested in prose. The sad thing about the human interest style is that, if that's not what I'm reading for, I begin skimming as soon as I detect it and much of the author's work ends up being for nothing.
- Florin_Andrei 8y ago
  Yeah, plain info versus story. Both have their uses.
jblow 8y ago
Amen. I am so tired of trying to read these articles that spend so much time on random personal backstories because they don’t have faith that the core subject matter is interesting to read. The worst are the ones that jump back and forth between A/B/C plots, jumping away before any satisfying conclusion is reached on any of them, as a way of tricking your brain into reading the article ... like a really bad TV show, or Westworld. All those articles can go burn in a hot, hot fire.

jniedrauer 8y ago

The non-deterministic nature of atomic decay by itself makes the universe unpredictable. And this is a thing that happens at STP. I think the author of this article might have forgotten that. There was never really any determinism to "save".

computerfriend 8y ago
General relativity is classical, so there is plenty of determinism to save.

8bitsrule 8y ago

As I recall, Gen. Rel. continues to explain all directly observable phenomena within limits of resolution. That's damn powerful. As for 'black holes', well ... believe what you choose. A prof. once told me that Einstein 'wasted 30 years' looking for unified theory. By that standard, so did Hawking I guess.