Naked singularities 

Recently my friends and I argued about what would happen if a singularity were to suddenly appear in the center of a room. I said it would be so dense we would probably be super condensed by its gravity, while my friend Tim said it would slowly draw the rest of the world into itself. My friend Matt said it would simply fuck up all our shit: west would become fish, fish would become cheese, and cheese would become the ultimate destructive power. Who if any among us is right? —Samuel Vasquez

HMM . . . I’d have to say Matt. Little can be said with certainty about singularities. However, we can reasonably surmise they would fuck up all our shit.

Couple issues we need to get sorted out. The first is assuming a singularity could appear all by itself—a so-called naked singularity. While theorists haven’t been able to rule this out, you really don’t want it to be possible.

The bigger issue is that you and Tim, at least, seem to be confusing a singularity with a black hole, a common mistake for space-time newbs. Allow me to explain.

A black hole is a region of space where matter has been packed together so densely its gravity is strong enough to keep light from escaping. Most people understand the general concept: you fall into a black hole, you get crushed to nothing, game over.

But there’s more to it. Once a black hole has formed, nothing can keep the matter inside it from continuing to compress till it reaches infinite density: a singularity. At infinity, the usual laws of nature are out the window. This has given rise to much woolly speculation:

• Our universe and everything in it was spawned by a singularity and may someday collapse back into one.

• A singularity could become a so-called white hole, basically a black hole that runs backward in time. This turns the second law of thermodynamics on its head and allows anything to spring fully formed out of nothing—an asteroid, a planet, destructive cheese.

You see where this is going: all our shit would be fucked up.

To avoid such things, theorists have come up with the cosmic censorship hypothesis, which posits that singularities aren’t allowed to go around naked in our universe; they’re always inside black holes. Remember, no light escapes from a black hole. If a singularity is behaving in a disruptive manner inside, who cares? Out of sight, out of mind.

Since we can’t usefully speculate about singularities, let’s turn our attention to black holes. What would happen if one were to appear in your living room?

The black hole would have to be physically tiny to leave you outside its event horizon—the boundary past which once you’re in, you don’t get out (although see below). Even outside the event horizon you’d have to be far enough away that the black hole’s gravity wouldn’t immediately suck you in.

Let’s assume you can resist a force equal to half of earth’s gravitational pull, or ½ g. If the earth was compressed into a black hole it would have a marble-sized event horizon, and would pull you into it with a force exceeding ½ g from a distance of about 5,600 miles.

Maybe Donald Trump’s living room is that big. Not mine.

A black hole the size of a hydrogen atom would contain as much mass as 1.6 times the water in all the Great Lakes and exert a ½-g pull from 2,000 feet away. Still no go.

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.

What happens if you get closer? The unpleasant phenomenon known as spaghettification. You’ll be torn to shreds by exponentially increasing tidal forces as you’re sucked into the black hole—32 g at one foot, 1,024 g at two inches.

How could a proton-scale black hole come to exist? The earth weighs 10 trillion times as much, but gravity hasn’t collapsed it to that size. What we need are some special circumstances. Options:

• When the universe was born, it’s thought many black holes of various masses were created, some of which may have shrunk to micro scale by now due to quantum thermal radiation, as predicted by Stephen Hawking in 1974. The likelihood of one drifting to earth, much less showing up in your living room, is on the order of once every 10 million years.

• Powerful particle accelerators could smash subatomic particles together, creating a tiny region of super high density. But the black holes thereby created would evaporate almost instantaneously.

In short, the odds of a close encounter with a black hole are vanishingly small. However, Hawking in a recent paper says black holes “should be redefined as metastable bound states of the gravitational field,” which I take to mean they may not necessarily be the one-way ticket to oblivion previously assumed.

In other words, whatever the quotidian vicissitudes, long-term there’s hope for our shit.


Send questions to Cecil via straightdope.com or write him c/o Chicago Reader, 350 N. Orleans, Chicago 60654.


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Cecil Adams

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