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?
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.
(Forgive the layman's attempt at understanding)
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!
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.
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.
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)?
[1]: https://www.wolframalpha.com/input?i=schwarzschild+radius+ca...
[2]: https://www.wolframalpha.com/input?i=%28red+blood+cell+size%...
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.
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
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.
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.
[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.
What if mysterious illnesses like fibromyalgia are just PBHs? Hmmm...
Aha! I finally know the cause!
Using Julia:
> using Unitful
> uconvert(u"W", Unitful.ħ * Unitful.c^6 / (15360 * π * Unitful.G^2) / (1.4e17u"g")^2)
18171.541554992324 W
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.
If it does not hit anything then mass does not really matter as long as small enough not to have big gravitional effect.
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.