Feb 122016

I saw a question on Quora about humans and gravitational waves. How would a human experience an event like GW150914 up close?

Forget for a moment that those black holes likely carried nasty accretion disks and whatnot, and that the violent collision of matter outside the black holes’ respective event horizons probably produced deadly heat and radiation. Pretend that these are completely quiescent black holes, and thus the merger event produced only gravitational radiation.

A gravitational wave is like a passing tidal force. It squeezes you in one direction and stretches you in a perpendicular direction. If you are close enough to the source, you might feel this as a force. But the effect of gravitational waves is very weak. For your body to be stretched by one part in a thousand, you’d have to be about 15,000 kilometers from the coalescing black hole. At that distance, the gravitational acceleration would be more than 3.6 million g-s, which is rather unpleasant, to say the least. And even if you were in a freefalling orbit, there would be strong tidal forces, too, not enough to rip your body apart but certainly enough to make you feel very uncomfortable (about 0.25 g-forces over one meter.) So sensing a gravitational wave would be the least of your concerns.

But then… you’d not really be sensing it anyway. You would be hearing it.

Most of the gravitational wave power emitted by GW150914 was in the audio frequency range. A short chip rising in both pitch and amplitude. And the funny thing is… you would hear it, as the gravitational wave passed through your body, stretching every bit a little, including your eardrums.

The power output of GW150914 was stupendous. Its peak power was close to \(10^{56}\) watts, which exceeds the total power output of the entire visible universe by several orders of magnitude. So for a split second, GW150914 was by far the largest loudspeaker in the known universe.

And this is actually a better analogy than I initially thought. Because, arguably, those gravitational waves were a form of sound.

Now wait a cotton-picking minute you ask. Everybody knows that sounds don’t travel in space! Well… true to some extent. In empty space, there is indeed no medium that would carry the kind of mechanical disturbance that we call sound. But for gravitational waves, space is the medium. And in a very real sense, they are a form of mechanical disturbance, just like sound: they compress and stretch space (and time) as they pass by, just as a sound wave compresses and stretches the medium in which it travels.

But wait… isn’t it true that gravitational waves travel at the speed of light? Well, they do. But… so what? For cosmologists, this just means that spacetime might be represented as a “perfect fluid with a stiff equation of state”, i.e., its energy density and pressure would be equal.

Is this a legitimate thing to say? Maybe not, but I don’t know a reason off the top of my head why. It would be unusual, to be sure, but hey, we do ascribe effective equations of state to the cosmological constant and spatial curvature, so why not this? And I find it absolutely fascinating to think of the signal from GW150914 as a cosmic sound wave. Emitted by a speaker so loud that LIGO, our sensitive microphone, could detect it a whopping 1.3 billion light years away.

 Posted by at 11:26 pm