By Henze, NASA [Public domain], via Wikimedia Commons

How close would I have to be to a black hole merger for the gravitational waves to kill me?

Short answer: You’d have to be so close that you’d be within the black hole.

Long answer: It’s official. On September 14, 2015, LIGO (the Laser Interferometer Gravitational-Wave Observatory) observed the gravitational waves from a binary black hole merger. Based on the frequency and amplitude of the gravitational wave signal, LIGO reported a 29 and 36 solar mass black hole merged 1.3 billion light years away, forming a 62 solar mass black hole [1].

An attentive reader might notice that 29 and 36 add up to 65, not 62. This is correct, and it tells us that 3 solar masses of energy were radiated as gravitational waves. Remember how E=mc2? Matter can be converted into energy, and that’s what happened here. In this case, 3 solar masses of energy is equivalent to the combined luminosity of about 5000 supernova, or a small galaxy made of TNT. This energy went into a wave, much like the ripples on the surface of a pond, which traveled out through the universe stretching and squeezing space and time.

When that wave passed the earth, LIGO measured it. More specifically, LIGO used a laser (the L in LIGO) to measure the distance to two mirrors, 4 km away from the source. LIGO spits the beam and recombines it like a Michelson-Morley interferometer (the I in LIGO) so if the distance to these mirrors change slightly LIGO will see the interference pattern shift.

The gravitational wave that was observed in September strained LIGO by 10-21 – this means those 4 km long arms were squeezed by less than a hundredth of the width of a proton. That’s an almost unfathomable level of precision. LIGO is most likely the most sensitive experiment ever built, and those mirrors are likely the most still objects ever manufactured by humans.

To give you a sense for how sensitive LIGO is, consider some of their sources of experimental noise. Seismic noise is a big one, but did you know that they are sensitive to tides? The daily ocean tides squeeze and compress the North Atlantic continental plate, producing a far greater strain on the detector than any gravitational wave [2, 3].

 

Anyway, you need a massive expensive detector to detect this wave on the earth because we are so far from the source. If you were much closer, you might even be able to feel the strain of this wave’s passing with your body. If you were even closer, that stretching and squeezing might be enough to kill you.

How close do you have to be for a gravitational wave to kill you? I had a hard time finding numbers about the fatal limit for stretching humans, which at first made me sad, but then it made me happy. It’s a good thing those experiments haven’t been done. Let’s assume that it will kill you if your body is extended by an additional 25% of its height.

Since the amplitude of gravitational waves decrease as 1/r  we can find how close to the merger the strain would be 0.25:

(10-21) × (1.3 billion light years) =  (0.25) × x

So x works out to about 50 km. That’s super close – we’re well outside the range that this calculation would be valid. It’s so close that you’d be within the event horizon of the final black hole! Any such person would have been killed by the black hole long before they’d be killed by any waves.

 

 


 

 

special thanks to /u/Silpion and /u/themeaningofhaste
image credit: NASA via Wikimedia Commons

 


 

 

Have a question? Send it to matt@quarksandcoffee.com