Great and powerful Cecil, excellent job once again on your article regarding black holes and singularities. You have gotten most of the important points correct; however, as a professor of physics I would be remiss to not point out your incorrect usage, equating the word force with the gravitational acceleration “g”. But alas! 'tis but an easy fix. Rather than stating “a force of g/2”, replace that with the phrase “a force that would cause an acceleration of g/2”.
For example, your weight is the force between you and the Earth, which is measured in pounds in British units, or in newtons in the SI unit system. Little “g”, is the downward acceleration on you (and everything else near the surface of Earth which is measured in feet per second per second (British) or meters per second per second (SI units). Little “g” is only valid near the surface of Earth, but it derives from Newton’s universal law of gravitation, which states that the force between any two bodies is directly proportional to the product the of their respective masses and inversely proportional to the square of the distance between them and is directed along a line connecting the centers of the two objects. The constant of proportionality has been measured experimentally and has been labeled capital or “big” G. For any object with mass “m” near the surface of the Earth, we consider the distance between the centers of the object and Earth to be approximately the radius of Earth. If you plug in the values of Earth’s radius R, Earth’s mass M, and the value of G, (G*M/R^2) in the proper units, which for SI is meters, kilograms, and seconds, you get about 9.81 meters per second per second or 32 feet per second per second. That value comes up so often that we label it simply little “g”.\
Last time I was at Lowell’s Observatory there were several crates labelled “BLACK HOLES.” (I would have enclosed a photo if I was allowed to post attachments.)
Apparently some observatories can get shipments of black holes for, um, experiments. Or something. Perhaps they are used in some sort of super-secret weapons program. In any event, I was able to approach the crates and even touch them without getting spaghettified, so either the black holes in them were very small or they had been removed for study. There wasn’t even any CAUTION tape around them.
I think Cecil could’ve done a better job of explaining what a singularity is as it is a little bit misleading to treat to singularities as if they were some sort of object in space. In the most general sense they are just some form or other of pathological behaviour in a spacetime, but mostly the term is used to describe geodesic-incompleteness. So a singularity just means that some observer’s point of view can’t be extended forwards or backwards beyond a certain point in their time. Sometimes this singularity seems to take the form of something that very much looks like a point in space (i.e. the singularity in a Schwarzschild spacetime), but there’s no reason to think that it is always as neat as this.
For that matter, wouldn’t a “proton-sized” black hole be expected to pump out Hawking radiation like crazy? Unless such a low-mass singularity can be stable (which can’t be ruled out), I’m thinking that spaghettification might be the least of your worries.
I’d recommend anyone who wants to learn about singularities read General Relativity by Robert Wald (it has a chapter on the subject). It’s heavy going (it’s a textbook), but I’d place it as one of my favourite books of all time as it explains things as simply as possible without insulting your intelligence.
Cecil said “exponentially increasing tidal forces” Is he sure?
Sure the gravitational field becomes ‘denser’ the closer you get to the mass centre and the pull on an external mass increases with proximity. However that’s exactly what happens with normal gravity from planets and that’s an inverse square law, not ‘exponential’ .
Getting onto ‘tidal forces’ They don’t actually exist. The tides we see on earth are a result of a divergent gravitational field (mostly from the moon). In crude terms the water on the far side of the earth is less gravitationally attracted to the moon than water on the moon-facing side due to the far side being further down the gravity gradient than the near-side. As a result we see similar but not identical water bulges on the near side and far side of earth.
As an aside I think I’m safe in saying that gravity is transparent to intermediate mass. That is, ignoring the gravitational effect of the intervening mass, the attraction between two bodies is the same whether or not there is a third mass between them.
The tidal force is M/r[sup]3[/sup]. Certainly not exponential. For a “normal” black hole, the point where a person would get torn apart is actually inside the event horizon, so all the nastiness going on at the event horizon is going to be a bigger problem. But for the objects Cecil is talking about, yeah, it’s an issue.
That depends on what you mean by a “normal” black hole. For a supermassive black hole such as is found in the center of a galaxy, a human could survive crossing the event horizon un-spaghettified (for a little while, at least). For a stellar black hole, a few times the mass of the Sun, not so. And there’s not actually any nastiness at the event horizon itself, at least not locally: It’s the point of no return, but you needn’t actually notice as you’re crossing it.
Quantum mechanics as we know it is mute on the subject. It is widely expected that, once we develop a theory of quantum gravity, it will predict effects which prevent the formation of true singularities… but since we don’t yet have such a theory, this is really only a guess.
But the area near a black hole is nasty. Extreme x-rays and such due to the accretion disk. The effects are especially more noticeable as you approach the event horizon. (And once inside … then there are different ideas.) And with a rotating black hole, frame dragging gets worse as you approach. I generally think of my black holes as rotating and not isolated. YMMV.
There are nasty effects in the general vicinity of a black hole, but the accretion disk (if there is one) ends well before the event horizon (and need not exist at all). And frame dragging certainly occurs, but it’s not a local phenomenon: You’d only notice by seeing that the distant stars seem to be twirling about you.
I thought this was a pretty good column. I hadn’t read the Dope in a while, and I was going to ask if Cece still has the same ghost, but I suppose we don’t do that here.
One passage in the column kind of jumped out at me, and I’m surprised neither Cecil nor anyone else in this thread commented on the obvious implications:
“A proton-sized black hole, though — that might work. It would weigh just 652 million tons, meaning you could approach as close as nine feet.”
So, never mind tidal forces and radiation and other hypothetical stuff. A small object weighing **652 million tons **has just materialized in the middle of your living room. It seems to me the first thing you are going to notice is this massive object crashing through your floor, probably followed almost immediately by the building collapsing around you. Observers at a safer distance would probably observe a crater forming where the house used to be (although the nature of this might depend on the local geology), and also a loud bang as air rushes into the empty space to replace the air that got sucked into the black hole.
Nine feet away would not be at all safe.
Meanwhile, the object continues to crush and displace soil as it gets pulled down towards the center of the Earth. I dunno, is there any kind of rock in the mantle that would be able to support a load of 652 million tons concentrated in a tiny point? I’m guessing probably not. So, on the bright side, you’ve solved the age-old problem of how to “dig a hole to China”.
I think you’re not realizing just how small a proton is. The mini-black hole would more or less pass through the earth like lead shot through a cloud. It’s tidal force would disrupt matter for a small distance (centimeters?) but the event horizon would be so small that very little matter could enter it. What you’d probably get is some seismic shock and a small channel filled with pulverized rock. In fact it would encounter so little resistance relative to it’s mass that the mini-black hole could probably fall to the Earth’s core, then climb out almost as high again, repeating for multiple cycles.
The earth is about 8,000 miles in diameter (near enough).
I assume being on the surface of the earth we cannot treat it gravitationally as a point particle. The far side is pretty far away and has a lower pull on me than the stuff under my feet.’
Is that seeming excessive gravitational pull here because in the case of a marble siced earth we can count it as a point particle? How far away from the earth do you have to be to mathematically be ok with treating it as a point?
