Comment by gotaquestion | Hacker News Reader

Comment by gotaquestion | Hacker News Reader

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> “let me explain something using terrible metaphors because I fail to understand the math myself”.

Some of these channels have millions of viewers, and the one I think you are referring to has 11M. Remember when the Reimann Zeta function summation of -1/12 was all the rage, or the Banach-Tarsky paradox? Google either of those and there are a dozen YouTube videos for each one. These are post-doctoral topics that become name-dropping buzzwords, I would never claim to understand these, yet people who watched the video do.

Which seems like a lot what the internet has given us: information, not knowledge. To quote a speaker I saw at Siggraph in ~1996, "Information is not power, knowledge is power." This hit home. We've seen it from people reading WebMD in the 2000's and then trying to teach their doctors, to the crazy scientific ignorance about mask mandates today. All because of internet edutainment or in the worst-case misinformation.

Anyway, yes, her article got cynical fast, but I think it was because she bounded with realism because plotted on the arch of technology evolution: it would take thousands of generations (even at an exponential pace) to create tech that can take actual measurements. That seems like good science to me.

I agree that most videos in YouTube simplify the problem too much or are just wrong. My recommendations anyway:

* Mathologer: "Ramanujan: Making sense of 1+2+3+... = -1/12 and Co." https://www.youtube.com/watch?v=jcKRGpMiVTw

* Vsauce: "The Banach–Tarski Paradox" https://www.youtube.com/watch?v=s86-Z-CbaHA

Each one is like half an hour long, but you may need to pause them and rewatch them a few times to understand the details.

Yes, I've watched both of those. Mathologer is in the biz of math, Vsauce is in the biz of ka-ching.

I don't think the vsauce channel is egregiously monetized. He sometimes does not upload for months or even years, and does not make the most clickbaity videos out there. He could've easily been much bigger than veritasium, in terms of monthly views, if he wanted to by just making the same type of videos as he used to do ( the broad mishmash videos that I really really liked honestly).

The fact that he didn't, to me, indicates he is obviously not in the business of making money.

Yeah, that's a good point. But I always found Vsauce and Ve to be clickbaity, with the former targeted at a more educated audience. But that's my opinion.

I am a fan of her work and videos but saying We will never make experimental progress on the black hole paradox for TEN THOUSAND years seems myopic at best. Does she not instantly realize how long that is? Unless we nuke ourselves out of it, I see us as an interstellar civilization easily within 100-200 years. That’s being conservative. I’d be surprised if we don’t have probes looking around the nearest black holes or even creating ones experimentally in double or triple digit years from today.

The closest good candidates for stellar black holes are thousands of light-years away from Earth. There is one possible candidate at about 1.1 kly, but there are good reasons to think that it (QV Telescopii) will turn out to be something else, as seems to be the case for LB-1 *. V616 Monocerotis at ~ 3.3 kly <https://en.wikipedia.org/wiki/A0620-00> is the closest thing that is virtually certain to be a black hole.

Given measurements of the Local Standard of Rest and star surveys of the LSR neighbourhood, it is unlikely that there are any stellar-mass black holes at all within about 300 light-years of Earth (and X-Ray astronomy and microlensing/MACHO-hunting surveys each gives even more pessimistic nearby black hole numbers) so the prospects of getting a signal from an Earth probe dispatched to close to a black hole within a millennium is, pardon the pun, faint. There could be only some thousands up to a few (~10) million in the Milky Way, a galaxy of hundreds of billions of stars at this point in its evolution. There may be as many as ten billion stellar black holes in and around Milky-Andromeda five or so billion years in our future.

I note you also say "creating ones experimentally", but that is in the realm of science fiction at this stage, barely hard s.f. even for microscopic masses, and it gets decidedly soft as one climbs up the mass scale from nanograms.

Fair, is it still theoretically possible that primordial black holes of mediocre sizes are floating around?

Also of course experimental black hole creation is in the realm of science fiction but so was going to the moon 150 years back. Question is if there’s a fundamental theoretical block , similar to FTL , in achieving it?

Primordial black holes may be floating around, but they are very unlikely to be any to be closer to Earth than stellar black holes, given the kinematic evidence. (There could be faint hope for an isolated one of a fairly small handful within the Milky Way. FWIW, I don't think there are small PBHs. There might be gargantuan ones in the universe. There definitely isn't one of those hiding in our galaxy though, but maybe in our galaxy cluster near the centre of mass, wherever that is (millions of light years away, at least). There are some huge central black holes in some local galaxies that may have been seeded as primordial black holes -- the mechanism of growth of such ginormous black holes is not fully understood yet)). So they aren't really going to help you reach your thousand-year deadline, absent FTL travel.

Some researchers have proposed semi-seriously that there could be a small black hole lurking at the outer margins of our solar system. That obviously could be reached within a thousand years in principle (depends on how far out it is, although it must be considerably beyond Neptune's orbit), but we are perhaps decades out from a detection of it, if it even exists. The idea is, however, one of many reasons to build telescopes that are mainly to be aimed at objects in our star's immediate neighbourhood, to do very sensitive mapping of the metric the solar system sources (or, in Newtonian terms, our sun's gravitational field and the disturbances planets, asteroids, and other objects impose on it), and to do "nanolensing" observations on objects at a variety of distances. The Vera C. Rubin Observatory's Legacy Survey of Space and Time is a step in that direction, and will eliminate many possible hiding spaces for a nearby black hole.

There is an upper limit on proper acceleration proportional to mc^3/h-bar for massive subatomic particles like electrons, from Caianiello (1984) <https://doi.org/10.1007/BF02748378> (free PDF <https://link.springer.com/content/pdf/10.1007/BF02748378.pdf>) arising from uncertainty relations. We have no hope of producing that kind of acceleration as even with the best possible superconductors an Earth-bound accelerator can manage much less than a millionth of that <https://arxiv.org/abs/quant-ph/0407115>, and we need to be much closer in order to make a black hole out of small charged particles. Large particles are even harder to accelerate extremely. We also have a power-density problem: what fuels such an accelerator? Alternatively, accelerating less extremely means much longer linear accelerators, or nearly equivalently, less curvature in a ring accelerator. I think we're looking at a ring about the diameter of the orbit of Jupiter, or a linear accelerator crossing a large chunk of the inner solar system, but that's just a guess (someone has probably worked out some comparable size for ultrarelativistic heavy ions (lead or gold) though).

So the tl;dr is that it's not impossible, and it's easier than trying to throw large stars at one another, but neither is really plausible within your 1000 years. And neither is easier than sending a probe to V616 Mon. and waiting several thousand years. And we might do better by making really good observatories in and around Earth. Technically we could do all three, I guess, but we're more likely to live long enough to see improvements on the results from the <https://eventhorizontelescope.org>.

And of course, what I said about your three-digit timeframe goes double (if you pardon the expression) for your two-digit one.

This line of thinking led me to a paper I had not read before (even though it has a tremendous number of citations and is reference (2) in his famous Black Hole Explosions? (evaporation) letter of 1974[1]), by Hawking (1971) <https://academic.oup.com/mnras/article/152/1/75/2604549> (PDF freely available there).

In this paper he considers the possibility that the universe is almost dominated by tiny (~ micrograms) black holes formed in the very early universe, persisting to the 1970s and leaving tracks in sufficiently large and sufficiently numerous cloud chamber detectors given sufficient time. (This was also decades before optical detectors like at SNOLAB, but incongruously after the Nobel prize for bubble chambers, although it was on the cusp of the activation of <https://en.wikipedia.org/wiki/Gargamelle> and the Big European Bubble Chamber -- he would have been aware of how close they were to activation, and results from smaller predecessors). Fascinatingly, several years after publication, conceptually similar papers were put forward for hunts for dark matter, even though it is impossible to extract from this Hawking 1971 paper that he was thinking of galactic rotation curves.

The paper also pre-dates evidence for the acceleration of the expansion of the universe, and contains the curious sentence: "An upper bound on the number of these objects can be set from the measurments by Sandage (7) of the deceleration of the expansion of the Universe." However, the excellent Allan Sandage paper of 1961 <https://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_que...> does not really let one take sides ("It suffices to say that no uncontested evidence is presently available [to choose between steady-state and expanding universe]") like Hawking 1971 seems to. Nevertheless, Hawking raises an interesting and slightly spooky premonition of dark matter at super-galactic scale, keeping clusters of galaxies looking like clusters over long periods of time, rather than separating into individual isolated galaxies: "This extra density could stabilize clusters of galaxies which, otherwise, appear mostly not to be gravitationally bound." In context Hawking was clearly thinking about a universe that grows into some very long term non-expanding/non-contracting configuration which includes clumps of galaxies.

Hawking 1971 tl;dr is "good luck actually observing these small weakly-interacting things, if they exist". Which is appropriate for 21st century particle dark matter experimentalists too. :^)

Penultimately, some patience with google scholar has found that a small handful of the many articles citing Hawking 1971 explore the idea of primordial black holes as dark matter. (but see below).

And finally, sometimes asking questions like yours (how does one build a very small black hole?) and taking them seriously leads to some very early, vague, ideas about how the universe might work in bulk, which is probably very very similar to what provoked Hawking's letter about 52 years ago.

- --

[1] https://sci-hub.se/https://doi.org/10.1038/248030a0

The relevant part of his evaporation letter: "There might, however, be much smaller black holes which were formed by fluctuations in the early Universe². Any such black hole of mass less than 10^15 g would have evaporated by now." In that context, I think a very low motivation for someone not terribly interested in the history of primordial black hole research to have previously hunted down a 1971 note whose idea was shortly thrown under the bus by its author is fairly understandable. :^)

Hawking 1971 is however an early note on primordial black holes (the only obvious earlier one in the literature is from Zel'dovich and Novikov in 1966), and that seems to be behind many of the citations I briefly sampled. Practically all also cite the more extensive follow-up Carr & Hawking 1974 "Black holes in the early Universe" <https://ui.adsabs.harvard.edu/abs/1974MNRAS.168..399C/abstra...> which is very close in submission date to the publication date of Hawking's "Black hole explosions?" yet does not appear to consider evaporation.

One refutation I’ve heard (in YouTube videos lol) for the possibility of a swarm of “small” pbhs floating around is that if one of them passes through a neutron star it instantly becomes a black hole - thus you can’t have densities high enough that they hit neutron stars often enough to take them all offline beyond the numbers we observe..

Neutron stars are rare and hard to hide (they're very bright in X-rays, and stand out against dim and dusty backgrounds, unlike isolated black holes). There are maybe low tens of thousands of neutron stars in the Milky Way (we've counted about 3000 of them).

There are hundreds of billions of regular stars in our galaxy (and in similar galaxies), some much more massive than neutron stars, and all of them have a much larger cross-sectional area than neutron stars. (NSes are tiny -- compare with New York City -- <https://commons.wikimedia.org/wiki/File:Neutron_Star_Manhatt...>) So small black holes are much more likely to collide with ordinary stars, and even Long Island NY and other comparable features on Earth, other solar system bodies, and exoplanets (we've counted five thousand of those now, and a lot of them are considerably closer than the nearest neutron star). But we see no evidence of that.

Again pardon my amateur source of the discussion - I learned this from A PBS space time video where it was contended that a fast traveling pbh with asteroid level mass wouldn’t actually slow down and just pass through most things like planets. But not neutron stars. Also I suppose stellar cores? No idea.

Although it's great that it's provoked you into asking questions, it seems like there is a lot that the PBS video must not be placing into your mind, like how these asteroid size masses are moving with respect to some local standard of rest in their region of the galaxy (and how commonplace they are) are crucial to the idea.

If they're moving gently along with all the stars in their neighbourhood, collisions between these asteroid-mass black holes and anything appreciable is unlikely (just as star-star collisions are very rare) that we wouldn't expect to see that ever happen.

Wandering pretty violently in comparison to nearby bright objects, an asteroid-sized black hole is likely to zip by a star and its satellites on a (strongly) hyperbolic orbit, like <https://en.wikipedia.org/wiki/%CA%BBOumuamua>, just dimmer. It's even less likely to hit a neutron star because of the NS's compactness, and because the geodesics it generates produces greater hyperbolicity near its surface (because that's quite near the centre of mass) than near the surface of a regular star. And hitting a sun-like star is already hard for an asteroid: <http://curious.astro.cornell.edu/our-solar-system/comets-met...> (likewise, we have never seen a small black hole flare up near our sun).

It is more likely that -- very occasionally -- an asteroid mass object (by strong equivalence principle, it does not matter if it is rocky, icy, or a black hole) is captured into a weakly hyperbolic orbit, or even an elliptical one, by a ~stellar mass. There are reasons to think an NS might be more efficient at this than a fatter star. But then you get a (possibly wide) binary star-BH that soon becomes hard to distinguish from a binary that formed together and "grew up" as stars together, with one happening to get too fat and collapse. The missing nebula in the captured-BH case would raise questions.

I don't buy the idea of a small black hole that somehow manages to slice through a neutron star doing much to the neutron star. Typically many many solar masses of matter fall back onto neutron stars after they violently form, and almost certainly there are asteroid-sized chunks of heavy atomic nuclei landing on them often. If you had some cosmic pool shark aim a small BH so precisely that it not only enters the (very very very very very small) NS core, but stays there, coming to a stop just so, the NS would collapse into the BH [1], because no matter can rest just outside the event horizon. The inner hard "platform" matter would fall in first, and in turn the freshly unsupported upper layers which had been "standing" on that platform would fall in, and so on down the widening drain. But if you shoot an asteroid-mass through an NS, it's hard to think there'd be much consequence. Sufficently slowly, there could be a nuclear explosion but probably not one that's catastrophic to the NS's integrity: I think it'd be hard to distinguish from the nuclear explosions from the rain of supernova-remnant material falling back down onto it, or random interstellar matter an isolated NS might encounter, or crustal quakes.

(I could be convinced by an academic paper equipped with an NS equation of state though (see [1] again), in principle, but very likely not a youtube video, much less a second-hand summary of one :-) ).

To a zeroth order approximation, the effect on a planet of a collision with an asteroid-mass black hole is not going to too different from the effect of a pair of collisions with ordinary asteroids (the "pair" is from the ingress and egress sides of the "tunnel": actual asteroids will tend hit a surface and stay there, or break up in a thick planetary atmosphere if there is one, etc., while small black holes will sail through). The asteroid-mass black hole will certainly create lots of electromagnetic interaction on contact; you can think of how black holes tend to have bright accretion structures, so you expect a big flashy kaboom as with a rock (but with more X-rays and gammas).

While we can resolve exoplanets, we can't quite see them being hit by asteroids, assuming the Jupiter-type exoplanets are hit with some frequency, we could blame limits in our telescopes. (JWST will help very soon!). Rockier exoplanets are no more likely to be hit by asteroids and lit up brightly than Earth or Mars. Asteroids are just tiny masses compared to these bodies.

- --

[1] fate of a neutron star with an "endoparasitic" small (and possibly primordial) black hole, that "just so" is already inside the NS: https://arxiv.org/abs/2101.12220

Got it. The reference is great, the only final addendum I wanted to mention was whether a neutron stars densities would stop a black hole in its tracks since the paper only talks about the black hole already having been there. (At least to remove the amateur recollection of mine from the reference link, the mention of this possibility happens in the video at 6:18 https://youtu.be/qy8MdewY_TY ) and here’s them talking about a BH punching through earth which seems roughly in line with what you say as well! https://youtu.be/AK44wAvv2E4

Thanks for the detailed reply, obviously I’m not from the field and most my knowledge is from YouTube so your refutations help. Will read up further for sure.

FWIW if I live long enough for someone to confirm that Planet X is a black hole I’ll strip naked and dance in Times Square because golly is that such an out of the blue hypothesis.

Is the OMG cosmic ray particle an exception to your acceleration limit? (Sorry tried to calculate the number with wolfram alpha and got lost in the dimensions). If so perhaps there’s a possibility of using cosmic rays to get around us being unable to make such fast particles?

The relevant quantity in ultra high energy cosmic rays (like OMG!) is the GZK limit (initials of a paper's authors), which is an upper limit on the energy-momentum of an intergalactic proton, set by interactions with charged matter and cosmic microwaves along the way, which transfer an UHEC proton's momentum to particles resulting from the interactions. OMG! is one of several curious possible violations of the GZK speed limit. (GZK does not deal with re-acceleration close to our galaxy via coupling to magnetic fields for instance, nor says anything about a galactic origin for something with cosmic-ray energies; it's all about how very fast protons can be slowed down over cosmological distances).

The highest energies of UHEC protons are probably not caused by "instant" accelerations as in a supernova (which certainly produces high energy protons that fly across the cosmos). Instead, they're more likely drawn up magnetically around the supermassive black holes powering active galactic nuclei (quasars, blazars and so on) and into jets, where they spend possibly weeks or accelerating through a natural counterpart to a particle accelerator which benefits from things like inverse Compton scattering (a hard X-ray from the black hole hits our proton boosting the proton's momentum and lengthening the X-ray's wavelength (i.e., reducing its momentum)).

But because we don't know OMG!'s origin, we can't say if OMG! tests any acceleration limit originating in uncertainty relations. Also, the Caianiello limit is unhealthy for protons (which OMG! likely was) staying protons: that they are composite structures makes them liable to be blown apart by extreme acceleration. Assuming it's a proton and had a blazar origin, OMG! is (really rough back-of-envelope work) likely to have fallen between 7 and 40 orders of magnitude short of the maximum (proper) acceleration. The intuition here is that OMG! is well short of Planck energy (by some 7 orders of magnitude) and super-high acceleration should take a proton from thermal energies to Planck energies. Of course a proton much closer to Planck energy could lose proportionally more along the way than a less-energetic proton, so who knows? There could be a doctoral dissertation waiting to be written on this!

Also, sorta disappointingly, OMG! could have had an electric charge greater than +1 (i.e., some ion with more than one proton) and in that case could have originated as close as our own sun <https://en.wikipedia.org/wiki/Solar_energetic_particles> <https://en.wikipedia.org/wiki/HZE_ions>.

You are amazing and I have learned so much here, thanks!

Popular science has leaned heavily on terrible, unhelpful metaphors for decades, long before any YouTube channel existed.

Of course you can't quickly teach the general public the actual math of quantum mechanics or whatever, but I think it's far far better to explain things in simple terms without further complicating the subject with awkward analogies.

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