Exploring Gravitational Waves: Feeling 10cm Distortion at 1LY

[DaveC426913]

Someone has raised an interesting discussion about how one might experience these waves closer to the merging BHs.

(Let's assume we're in a heavily-shielded spaceship that will protect us from all EM radiation and other effects except gravity.)

First, how big?
My back of napkin calculations suggest that, at a distance of one light year, a strategically-placed LIGO Mark II might detect a distortion of as much as 10cm.
(We on Earth are detecting a distortion of 10^-19m. LIGO Mark II, at one billionth the distance, the distortion should be a billion billion (10¹⁸) times as powerful. So LMII should detect 10^-1m distortion?)

Second. If that passed through you, would you simply feel a pull of 10cm, or would the shift happen at the speed of light, and turn you into a cloud of atoms?
By the equivalence principle, would you experience high acceleration? Well, I guess, yes, but one every atom simultaneously.

 

[jedishrfu]

There's an interesting distinction between gravity waves and gravitational waves:

http://news.discovery.com/space/gravitational-waves-vs-gravity-waves-know-the-difference-160208.htm

I hope you don't mind, I've adjusted your thread title accordingly.

 

[DaveC426913]

Thanks. I've actually noticed this discrepancy. In unrelated places, I've been seeing lots of meteorological "gravity wave" pictures and wondering if the term is sloppy. It seems not.

 

[pervect]

Someone has raised an interesting discussion about how one might experience these waves closer to the merging BHs.

(Let's assume we're in a heavily-shielded spaceship that will protect us from all EM radiation and other effects except gravity.)

First, how big?
My back of napkin calculations suggest that, at a distance of one light year, a strategically-placed LIGO Mark II might detect a distortion of as much as 10cm.
(We on Earth are detecting a distortion of 10^-19m. LIGO Mark II, at one billionth the distance, the distortion should be a billion billion (10¹⁸) times as powerful. So LMII should detect 10^-1m distortion?)

Second. If that passed through you, would you simply feel a pull of 10cm, or would the shift happen at the speed of light, and turn you into a cloud of atoms?
By the equivalence principle, would you experience high acceleration? Well, I guess, yes, but one every atom simultaneously.

I'm not sure of the relation between strain as measured by Ligo, and effective power (averaged over a cycle) in the gravitational wave. I'm thinking that if h is the strain, the effective power is proportional to ##\left( \frac{dh}{dt} \right)^2##, but I am not at all confident, I don't work with gravitational waves enough. If that is correct though, your estimate is too high.

Maybe we can get someone else to comment.

 

[PeterDonis]

at a distance of one light year, a strategically-placed LIGO Mark II might detect a distortion of as much as 10cm.

That's a 10 cm distortion in a 4 km long interferometer arm. (I'm actually not sure about the 10 cm number; see below.) The distortion in a smaller object, like you, would be smaller in proportion to the size of the object. In other words, GWs induce distortions in an object of a certain fraction of the length of the object. The GWs recently detected by LIGO induced fractional distortions in the interferometer arms of about ##10^{-21}## (I think); a LIGO Mark II that was one light-year away from a similar merger would receive fractional distortions 18 orders of magnitude bigger, or about ##10^{-3}##. In a 4 km arm, this would correspond to a length change of a meter or so. But in your body, with a size of order 1 m, the induced distortion would be a millimeter or so from one end of your body to the other.

Actually, even that isn't quite right, because your body's atoms are held together by strong interaction forces, whereas the mirrors at the end of LIGO's arms are not--they are supposed to approximate free motion as closely as possible given that they are at rest in the Earth's gravitational field instead of floating in deep space. So LIGO's arms manifest the effect of GWs entirely as length changes in the arms; whereas your body will manifest most, if not all, of the effect as an increased stress between its atoms--more precisely, as oscillating tensile/compressive stresses in different directions, as the forces between the atoms resist the GWs trying to pull them apart/push them together.

would the shift happen at the speed of light, and turn you into a cloud of atoms?

My initial guess is that the induced stresses would be well within your body's capacity to resist them; it might feel something like being on one of those carnival rides that shake you in rapidly changing directions.

By the equivalence principle, would you experience high acceleration?

Tidal gravity, in and of itself, does not cause any proper acceleration; its effects can be seen in the relative motion of objects in free fall. For example, the planned follow-on to LIGO, the LISA space-based interferometer, would have the mirrors at the ends of its arms in free fall, feeling zero acceleration, even when they were responding to GWs. (LIGO's mirrors are obviously not feeling zero acceleration since they are at rest in the Earth's field, as I said above; but the goal is to make sure they feel no additional acceleration over and above that.)

In an object like your body, whose atoms are bound by interaction forces, tidal gravity does cause different parts of the object to feel different accelerations, even if the object's center of mass is in free fall. But I'm not sure how relevant the equivalence principle is to the analysis of this kind of scenario.

 

[DaveC426913]

in your body, with a size of order 1 m, the induced distortion would be a millimeter or so from one end of your body to the other.

Yeah, I didn't account for the final 10^-3 scaling down to a human.

This article uses some different math:
http://www.forbes.com/forbes/welcome/#ac39ffb4aac3Then again, that is occurring at audible frequencies - meaning between 100 and 10,000 cycles per second.

Your body would ring like a tuning fork!

Actually, even that isn't quite right, because your body's atoms are held together by strong interaction forces, whereas the mirrors at the end of LIGO's arms are not-

While the body may be held together by those forces, that doesn't change the strength of the fluctuations trying to separate them. They would be put under that strain.

 

[PeterDonis]

Your body would ring like a tuning fork!

A purely solid object with high tensile strength would, yes. But the human body is not at all like that; it's a big squishy bag of fluid. Imagine shaking a big bag of water at 100 to 10,000 cycles per second with a fractional amplitude of ##10^{-3}##; mainly what would happen is that you would heat it up a bit.

 

[DaveC426913]

A purely solid object with high tensile strength would, yes. But the human body is not at all like that; it's a big squishy bag of fluid. Imagine shaking a big bag of water at 100 to 10,000 cycles per second with a fractional amplitude of ##10^{-3}##; mainly what would happen is that you would heat it up a bit.

Bad analogy.

Remember, the gravity waves affect every atom virtually simultaneously - more like being put in a microwave oven, wouldn't you say?.

(What power of microwave radiation would be enough to vibrate your atoms with an amplitude of a millimetre??)

 

[Keith_McClary]

(Let's assume we're in a heavily-shielded spaceship that will protect us from all EM radiation and other effects except gravity.)

If there were no accretion disks, just black black holes, would there be EM radiation and other effects ?

 

[PeterDonis]

(What power of microwave radiation would be enough to vibrate your atoms with an amplitude of a millimetre??)

The atoms don't move by a millimeter; that's the fractional distortion over the length of your whole body. Individual atoms will be distorted (in the absence of restoring forces) by about ##10^{-3}## of their own size, which would be about ##10^{-13}## meter. Separations between neighboring atoms will be distorted (again in the absence of restoring forces) by about ##10^{-3}## of the average separation between neighboring atoms.

 

[Orodruin]

Actually, even that isn't quite right, because your body's atoms are held together by strong interaction forces

Just going to nitpick a bit here. This could read the wrong way as it seems to imply that strong interactions are responsible for holding atoms together. Of course, those interactions are electromagnetic, but strong compared to gravity. It is worth pointing out that strong is here just being used as an adjective.