This is how close you'd have to be to feel a gravitational wave
In case you missed it, we heard the universe wiggle last week.
Einstein predicted back in 1916 that it's possible for anything with mass to ripple spacetime - basically, expand and relax like a speedboat's wake as it accelerates across a lake. He called these ripples "gravitational waves" and when the most precise measurement ever taken by human beings sensed them, it was a huge freaking deal.
But all this kerfuffle in the astrophysics world got Scott Aaronson, a theoretical computer scientist at MIT, wondering: What would it take to actually feel a gravitational wave?
Aaronson posted some back-of-the-envelope calculations on his blog, Shtetl Optimized, which is very popular, or at least in two-advanced-degrees-and-counting corners of the internet.
Every object with mass creates gravitational waves, but they are so faint (or, as Aaronson puts it, the universe's Sleep Number is so high) that most are imperceptible from any distance. It took a collision of two black holes 1.3 billion light years away to trip the world's most sensitive sensor.
Aaronson used that collision as a benchmark:
By now, we all know some of the basic parameters here: a merger of two black holes, ~1.3 billion light-years away, weighing ~36 and ~29 solar masses respectively, which (when they merged) gave off 3 solar masses' worth of energy in the form of gravitational waves-in those brief 0.2 seconds, radiating more watts of power than all the stars in the observable universe combined. By the time the waves reached earth, they were only stretching and compressing space by 1 part in 4×1021-thus, changing the lengths of the 4-kilometer arms of LIGO by 10-18 meters (1/1000 the diameter of a proton). But this was detected, in possibly the highest-precision measurement ever made.
In other words, the enormous power of two black holes colliding is undetectable in your body from over a billion light years away.
But what about, say, the distance from the Earth to the Sun?
It turns out gravitational waves dissipate very fast, at a rate proportional to their distance from their source. (You can find the technical details here if you're curious and physics-literate.)
So, if you were as far from the black hole collision as you are right now from the sun, Aaronson found the gravitational waves would distort your body by about 50 nanometers - nowhere near enough to feel. (He repeatedly notes these calculations are very rough.)
Next he checked for a distance of 3,000 miles, or about how far New York City is from Los Angeles. That would distort your body by about a millimeter. "Would you feel that?" he writes. "Not sure."
There wouldn't be even a centimeter of distortion in your body until you were 300 miles away - at which point you'd certainly have other problems. Like being ripped to shreds by the gravity of two merging black holes.
Here's Aaronson's takeaway from all of this:
People often say that the message of general relativity is that matter bends spacetime "as if it were a mattress." But they should add that the reason it took so long for humans to notice this, is that it's a really friggin' firm mattress, one that you need to bounce up and down on unbelievably hard before it quivers, and would probably never want to sleep on.
He ends his take by reiterating that he's not an astrophysicist (author's note: he is very, very smart), and inviting more knowledgeable scientists to critique his calculations.
"Public humiliation, I've found, is a very fast and effective way to learn an unfamiliar field."
You can find Aaronson's original blog post here.