
Mathematicians Disprove Conjecture Made to Save Black Holes - bainsfather
https://www.quantamagazine.org/mathematicians-disprove-conjecture-made-to-save-black-holes-20180517/
======
habitue
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.

~~~
mikekchar
It's not just science reporting. One of the reasons I hate the Olympics is
that I like to watch sports on TV: Not heartfelt stories of overcoming
adversity to become one of the world's elite. Not teary eyed medal ceremonies
with semi transparent backdrops of national flags blowing in the wind. Not
endless medal count standings. Not interviews of people with three medals
around their necks, with insets of proud parents in the upper left hand
corner. I just want to see the sporting events.

Today's society values drama above everything else. It's a shame (either that
they do, or that I don't fit in ;-) ).

~~~
alasdair_
I really liked watching the original Ninja Warrior (the Japanese version). I
even liked (to a lesser extent) the first US-heavy version.

I stopped watching for exactly the reason you describe.

The exact same thing happened with esports. Five minutes of actual play, 25
minutes of fluff.

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nerdponx
_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
Einstein and Penrose theory totally crushed by mathematicians -- that makes a
better headline.

~~~
nerdponx
"Einstein and Penrose were wrong; this is why"

~~~
philipov
"10 crushing proofs Einstein and Penrose don't want you to know" : Best
headline.

~~~
diegoperini
What color is this proof: Einstein or Penrose?

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bencollier49
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
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
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
"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.

~~~
pofilat
What is f'(0), the derivative of f at 0? It _doesn 't even exist_, therefore
it has no discontinuity at 0.

Darboux's theeorem says that there is no way to create a jump in the
derivative, in part because a derivative at a point is defined in terms of
limits from _both_ sides, so the limits must be the same.

~~~
thaumasiotes
> What is f'(0), the derivative of f at 0? It _doesn 't even exist_, therefore
> it has no discontinuity at 0.

This is definitely wrong. The derivative of |x| is -1 where x < 0, and 1 where
x > 0, and doesn't exist where x = 0. That is a perfect match to the
definition of a jump discontinuity -- the limit from the left is not equal to
the limit from the right.

It's not at all necessary for the function to exist at x = 0 in order for it
to have a discontinuity at x = 0.

But hey, don't take my word for it; why not check the definition on Wolfram?

[http://mathworld.wolfram.com/JumpDiscontinuity.html](http://mathworld.wolfram.com/JumpDiscontinuity.html)

The original claim was "the derivative, if it exists, cannot have a jump
discontinuity." This is badly stated. You're defending the idea that if the
derivative exists _at a particular point_ , then there is no jump
discontinuity in the derivative _at that point_. But there can be a function
_f_ which satisfies both of these properties:

\- _f_ is the derivative of some other function _F_. ("The derivative of _F_
exists.")

\- _f_ has a jump discontinuity, somewhere. ("The derivative of _F_ has a jump
discontinuity.")

~~~
disconcision
The definition you link states that a function has a discontinuity at a point
/in its domain/ if yadda yadda. 0 is not in the domain of f'. See for example:
[https://math.stackexchange.com/questions/1431796/if-a-
functi...](https://math.stackexchange.com/questions/1431796/if-a-function-is-
undefined-at-a-point-is-it-also-discontinuous-at-that-point)

~~~
thaumasiotes
That is a question of your personal focus. For example, I'd expect a theorem
that applied to "functions from ℝ to ℝ" to apply to f(x) = 1/x unless a
specific qualifier was given.

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jryan49
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
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.

------
jniedrauer
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
General relativity is classical, so there is plenty of determinism to save.

------
namibj
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
> [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.

~~~
monocasa
> In modern physics of this type, where experimentation is not practical, the
> math is the physics

I think Feynmann would disagree with you.

[http://www.youtube.com/watch?v=obCjODeoLVw](http://www.youtube.com/watch?v=obCjODeoLVw)

~~~
mlevental
feynman died 30 years ago. it's plausible the culture of the field has changed
(nm that feynman wasn't the arbiter of culture to begin with)

~~~
JadeNB
> it's plausible the culture of the field has changed (nm that feynman wasn't
> the arbiter of culture to begin with)

To be fair to monocasa's objection
([https://news.ycombinator.com/item?id=17101892](https://news.ycombinator.com/item?id=17101892)),
the rebuttal was not of a claim that the _culture_ of physics was mathematical
but literally of my claim that (certain) physics _was_ mathematics.

------
8bitsrule
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.

------
nyc111
> 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.

~~~
qubex
I am quite stupefied by this statement. NASA and other organisations most
certainly uses _Classical_ mechanics (whether in its Newtonian, Lagrangian, or
Hamiltonian formulations does not impinge upon the central issue) when
simulating celestial motions and calculating trajectories. That there exists
an acknowledged ” _Three Body Problem_ ” ( _i.e._ , that the trajectories
followed by more than two bodies interacting gravitationally are in general
not algebraic) matters not one iota for _numerical_ simulations such as those
performed by aforementioned organisations for aforementioned purposes. Some
kind of relativistic correction might be made for motions that occur within
the orbit of Mercury, but again, those are numerical in nature. And as far as
I know there are no exact solutions known for general-relativistic
interactions between two gravitational objects, placing it at an even greater
’disadvantage’ compared to the ’Newtonian’ mechanics you erroneously deplore.

~~~
nyc111
> matters not one iota for _numerical simulations_ such as those performed by
> aforementioned organisations for aforementioned purposes.

So you agree that planetary orbits are computed by numerical simulation as I
claim. Then why do you object at what I'm saying?

