10^17g is about 20,000 times heavier than the great pyramid of giza. Funny to imagine something as massive as a pyramid pass through your body and not noticing it.
Is the difference that a massive objective hitting you would typically do damage via the electromagnetic force?
But if you consider the gravitation force of the pyramids obviously that's extremely weak compared to the other forces on our body, so we shouldn't expect it to do damage in the same way?
Remember that gravity falls off in strength with the square of distance. The gravitational field around such a black hole would be immensely strong and absolutely miniscule. The event horizon would be the size of a few atoms.
Locally, the black hole would swallow any atoms it comes into contact with and would probably scatter nearby molecules, but that's it. It'd pass straight through you.
The gravitational field would be enormous: 1,000–500,000 times Earth gravity, at one meter's distance, for the range of PBH masses this paper mentions. That's balanced out by the relative speed being a brisk 200 km/s, so the interaction time would be short (microseconds). Still a pretty significant momentum impulse if one flew by.
This is analyzed in the paper. There are two sources of problems: gunshot-wound-like, and the effect of transiently highly increased gravity on nearby tissues. The first one seems worse, and is the limiting factor. PS. The paper is very easy to read :)
If Bob is floating in space in a capsule, and a very heavy asteroid floats past, the amount that Bob's capsule is moved is dependent on the speed of the asteroid?
Does that sort of thing have to be considered when planning the orbits of probes etc?
Is Earth traveling fast enough, from the viewpoint of Alice floating near the sun, to have a gravity "tail" or "wake" trailing after it? (Alice near the sun thing is my attempt at a mostly static observer) And of course due to relativity, if Alice was orbiting retrograde to the big heavy object, she'd observe even more effect?
I think I need about 6 more cups of tea before I can think about this!
> If Bob is floating in space in a capsule, and a very heavy asteroid floats past, the amount that Bob's capsule is moved is dependent on the speed of the asteroid?
Yes
> Does that sort of thing have to be considered when planning the orbits of probes etc?
Yes, it's a primary concern when sending probes to other planets
> Is Earth traveling fast enough, from the viewpoint of Alice floating near the sun, to have a gravity "tail" or "wake" trailing after it?
If I understand you correctly, then classically (i.e. ignoring relativity), no. Your gravitational acceleration towards the earth depends only your distance to it. If you consider general relativity? It's... complicated.
Force is the derivative of momentum. If you apply a gravitational force for a short time, the derivative is the same but the change of momentum is tiny. If you apply it for a longer time, the change is bigger.
> Locally, the black hole would swallow any atoms it comes into contact with and would probably scatter nearby molecules
More likely, it would go straight through most atoms without interacting with them. They are tiny and move very fast, if you do the math the likelihood of direct, non-gravitational interactions with matter are somewhere near neutrinos, of which trillions passed through you while reading this sentence.
When one does end up eating something, the most significant effect is probably that it wouldn't eat the whole atom, but either just the nucleus, freeing all the electrons, or just an electron, leaving the atom positively charged.
I wonder what happens to the electrons when/if they interact with the black hole. There's already weird stuff going on there with electrons being particles and waves. So, I wonder what happens when you introduce something like a black hole to the equation. Does it have a charge? I'm assuming it'd break through the electron shell; would it absorb the electron/s upon interacting with the shell?
> Locally, the black hole would swallow any atoms it comes into contact with
Would it be capable of doing that? If the radius of the event horizon is significantly smaller than the radius of a proton, would it be capable of swallowing a proton (and how)?
>Is the difference that a massive objective hitting you would typically do damage via the electromagnetic force?
Yes. PBHs, if they exist, have been constrained to asteroid mass ranges, and at the 10^17g the author concludes would be harmful, their radius would be 0.15 femtometers, or about 1/5 the radius of a proton. Combine that with galactic orbital speeds, and it's just too small and too fast to leave a mark, unless the mass is multiple mountains worth.
I thought this effect would dominate too, but it turns out the paper’s assumptions is that the PBH moves at 100 km/s so we’re talking about 5 joules while it’s inside you and maybe 1000 joules total while it’s in your vicinity. Hardly blood boiling stuff.
It's important not to blow off a few joules when you're speaking of radiation. The LD50 dose for a 75 kg human is only about 375 J (5 Sv) of gamma rays[1]. In this case, the 5 J delivered inside you (I didn't check your calculations on this, just using your number), and perhaps another 5 on approach and exit, only end up being about 10 J (0.12 Sv), which is not enough to kill, but it is still a rather large radiation dose. It's more than twice the annual limit for occupational safety in the US, and is near the lower limit of the dose that could cause acute radiation syndrome. If the hole passed directly through your digestive tract, concentrating the dose in the vulnerable tissues there, there's a decent chance you'd get mildly sick.
[1] Gamma rays have a weighting factor of 1 in the gray -> Sv calculation, and the black hole emits them isotropically, so they're roughly distributed across the body. So in this case, 1 Gy ~ 1 Sv.
I agree. Absorbing 100 J (the paper's assumption) over an entire 75 kg body would be ~1.3 Gy whole-body dose, or 1.3 Sv for photons. That would probably make you sick. Traditional radiation therapy for cancer delivers 2 Gy/day x 30 days to the tumor to kill it.
What if mysterious illnesses like fibromyalgia are just PBHs? Hmmm...
The assumption in the paper was 100km/s which is definitely hyperbolic.
If you slow it down to solar escape velocity at the Earth (the borderline of what you might expect) you get 42km/s which is only a bit slower than in the paper. This would mostly have the effect of doubling your radiation exposure.
I believe black holes are not currently emitting any Hawking radiation, because the CMB is far too hot for now. They will start emitting Hawking radiation in the far future, after the Universe has cooled down significantly.
Black holes emit Hawking radiation regardless of ambient temperature. It's just that right now, the mass(-energy) of photons falling into the hole from the CMBR is outpacing the mass loss to Hawking radiation for large black holes, so large black holes aren't currently evaporating from their own Hawking radiation.
It's like standing next to a campfire. Your body is still emitting thermal radiation in the IR, it's just that you're receiving more thermal radiation from the fire than you're putting out.
I think the idea is that black holes can never shrink to a size small enough to emit a hawking radiation hotter than CMB as long as it receives photons from the CMB that that will balance the mass/energy of the black hole and keep it in equilibrium.
This obviously is not a problem if you create a new very small black hole from scratch as it only applies to pre-existing black holes that are massive enough so that their hawking radiation temperature is lower than the CMB
Because a black hole of that mass would be tiny (smaller than a micrometer according to the article), and gravity is a very weak force. It would pass through you like through butter and bore a tiny tunnel, but it's so small it would probably leave you unharmed.
I know this is just an idiom, but it got me to thinking about just how much easier it would be for the PBH pass through you than a knife through butter. Some back of the envelope calculation gets me 40 orders of magnitude. If you compare the ease of a knife through diamond to a knife through butter, even that difference is many orders of magnitude less than a PBH through the human body.
Because it isn't big. It's massive. Those are not the same thing. Our everyday intuitions deal with solids with densities within a couple of orders of magnitude (from very light foamy solids at perhaps 0.1 g/cm^3 to very dense metals around 20 g/cm^3), so the two can never be that far apart in everyday experience. But small black holes are many, many, many, many orders of magnitude denser than that.
When a big solid object (where "big" is "macroscopic") strikes your body at a low speed (where "low" is "a few km/s"), it interacts with the atoms in your body. It applies pressure to your body, primarily the degeneracy pressure[1] that pushes back when electron clouds push up against one another. The interaction tine is long (on the order of milliseconds to seconds), so not only is the applied force high, the force has time to do its work. The push overcomes the mechanical strength of the structures in your body, like the walls of your blood vessels or the membranes of your cells, shattering them and causing the secondary damage of bleeding, organ dysfunction, inflammation, vulnerability to infection, etc.
When our black hole here passes through you, though, it is both extremely small (smaller than an atom, if by "size" we mean its event horizon) and moving extremely fast (about ten times Earth's orbital velocity, or about a hundred times faster than a bullet).
It's too small to directly "eat" your tissues, and it isn't "pushing them out of the way" by much, either. It interacts with your body by tugging on it. That tugging would be enough to tear your body's structures apart if it were sustained (the tidal forces here are very extreme), but the hole is moving so quickly that while the force is very large, the impulse (force times time) is not. It does devastating damage along the very narrow corridor where it's munching up an atom or three as it goes and where it's applying ultra-extreme forces that matter even over these millisecond timescales, but the corridor of damage is so narrow that it doesn't disrupt the function of your body. (The paper establishes the mass cutoff where this would no longer be so, and where the gravitational shockwave would indeed be enough to start tearing at your body's structures.)
It's kind of like how you can snuff out a candle with your fingers, even though a typical candle flame is not much cooler than the surface of the Sun. The heat flux from the flame to your skin is extreme, but it's applied for such a short period of time that the total energy delivery is tiny and does not deal meaningful damage to the skin.
[1] Electrostatic repulsion plays a role, but degeneracy pressure is the primary thing that makes matter take up space.
The Schwarzschild radius is 2 G M / c^2. When we assume the cutoff mass of 1.4e14 kg, then the Schwarzschild radius would be 103.966e-15 m ≈ 104 femtometers. A hydrogen atom has a radius of ~ 53e-12 m.
high speed means that their is no momentum spread through your tissues. the damage will be the diameter of the thing and this is rather small diameter.
Also related: Anatoli Bugorski, a Russian retired particle physicist, known for surviving a radiation accident in 1978, when a high-energy proton beam from a particle accelerator passed through his head (https://news.ycombinator.com/item?id=42213629)
If that's the second most embarrassing thing that happened to you this week, and the first is something that only nearly happened, then I'd say it's been a good week.
Thank you so much for this! Never heard of it till I read your comment. Gonna watch it tonight. Bonus: Mary-Louise Parker, one of my favorite actors, stars.
David Brin's Earth also posits an experiment that drops a micro black hole into orbit of the Earth's core that goes undetected for some time until it accumulates enough mass to cause problems. Notably, it also predicted glassholes.
Would such "tiny" black holes be stable? I'm thinking Hawking radiation, or indeed the opposite, growing without bounds.
If they are, are they considered as possible "particles" for dark matter? I guess that's what MACHOs are? And won't interact electromagnetically, only really by gravity.
Small black holes can be stable if they have a charge or high angular momentum. These are called extremal [0] black holes - the charge and/or angular momentum counteract the hawking radiation. Some physicists have argued that electrons (stable, very tiny) could technically be described as super-extremal black holes [1]
Hawking radiation gives you a lower bound for the size of a primordial black hole that still exists, at 10^15 g. Primordial black holes largely cannot grow, because they would be traveling very fast, likelihood of interaction with ordinary matter is very small, and there is no mechanism that would slow them down.
So if there are some in our galaxy, they would just be zipping about at intergalactic speeds until the heat death of the universe, or until they hit the event horizon of a larger black hole and get absorbed. The present-day universe is just too sparse for them to form or accrete material.
Not necessarily. That is only the case for black holes with no charge and angular momentum. Given high enough charge and angular momentum for a given mass, black holes become "extremal" and their hawking radiation/temperature approaches zero. It's argued these are unstable or maybe can't even exist for various reasons, but it's a pretty active area of physics AFAICT https://www.quantamagazine.org/mathematicians-prove-hawking-...
That said, if these were primordial I'd expect their charges to not all be 0, so they'd interact with normal matter.
> "The number density of primordial black holes with a mass above this cutoff [MP BH > 1.4×1017g] is far too small to produce any observable effects on the human population."
For as long as I can remember I've had these random hyper-local sharp pains on my body. By the time I register them they're gone. I've always wondered if they were some particle passing through me. I don't know enough about anatomy to know how big something has to be to hit a nerve and have it register it.
Okay, so detecting damage to people from PMBs would be difficult. People are fairly difficult to work with as a specimen anyway, so wouldn’t a more meaningful study be “what easily detectable evidence would be imparted by one?” Holes in silicon wafers?
Oh man, so many questions! Would a PBH passing close enough to Earth to hit a human end up being drawn to the Earth's core or the Sun? Or would the mass/inertia of a rogue PBH be enough to keep it from falling into a local gravity wall and gobbling up the solar system?
Any object that approaches the Solar System from interstellar space is necessarily moving at least (solar) escape velocity. It's "falling down" into the Solar System's gravity by a distance equal to how far it has to "climb up" to get away in a system with little appreciable friction.
The paper assumes 100 km/s, which is more than double the solar escape velocity at Earth's orbit. The mass doesn't make a difference in the absence of friction and assuming it is much less than the primary body; escape velocity depends only on the mass of the primary.
There would be some "friction" (since the hole would be eating up small amounts of mass on its journey and that mass would be moving at less than solar escape velocity), but without doing any calculations I'm almost certain it's nowhere close to enough to slow it down.
An anecdote from one of my former physics professors was that there are theories that PMBs are being constantly generated and annihilated near-instantaneously all over the universe and that odds are astronomically low but one could form inside your body and be so far away from the nearest subatomic particle that it would starve out immediately.
Of course, the very concept of a black hole is still technically only the "best theory" to explain observed gravitational and radio anomalies, so it's always helpful to remember as a layman how distant from us this stuff truly is.
Besides being funny this paper also has some points - for example we know that no human has yet died due to a PBH passing through their body, but they very likely would had one passed through them. So that's sort of evidence against their existence. Although the estimated number (estimated towards the end of the paper) of such events per year would be utterly small anyways.
Hanlon’s Razor suggests no reasonable pathologist would ever label a death as caused by a PBH. It could have happened, but the effects probably looked similar enough to something more common for such deaths to be mislabeled.
There is a range of PMBs masses not currently excluded by observation that may explain dark matter, but if dark matter consists of PMBs in that range we're talking on the order of single digits in the solar system per century, not PMBs streaming through you like crazy.
New fear unlocked :) seriously though, is it true that a black hole can be as dense as it wants and still be smaller than an atom? at that point (pun intended), how do we even measure its size, given that it bends the space around it?
Until this study was done, we did not know if these objects could have affected humans. Imagine if they _had_ discovered the ability of PBHs to e.g. puncture a lung, blood vessel, or brain synapse. Maybe we would better understand e.g. crib death, or Alzheimer's disease.
Wouldn't any parent line their baby's crib with the mass equivalent of a million aircraft carriers in lead, to protect them?
I think that lead would be a bad material to use, considering a baby's propensity to put everything within reach into their mouths starting at a couple of months of age when they can start reaching. When they start teething they will inevitably start chewing on the soft metal.
We have a hard time understanding what dark matter is. There are theories that some of the dark matter could be tiny black holes left over from the big bang, called primordial black holes (PHBs).
How can we detect PHBs if they exist? If they existed in large numbers, would we notice them? The paper says that you would notice a PHB if it went through you, since you would likely die. We are not noticing people dying by mysterious gunshot-like wounds without guns in any large amounts, so there can not be that many PHBs around.
The paper is (weak) evidence against a large amount of PHBs. The paper is also slightly funny.
