The detectors are a big L-shaped pipeline that lasers bounce around in. Doesn't that just measure the X and Y axis of gravitational waves? What about Z-axis? Shouldn't they drill down as far as they can and add another arm?
Yes, each detector in itself cannot detect a wave going perpendicular to the two arms.
However, the two detectors that make up LIGO are oriented differently. In addition there's the VIRGO detector in Italy and more detectors being built.
With multiple detectors you can not only measure in different orientations, but also consider the difference in detection time between the detectors. So by combining data you can really narrow it down.
You can see an example of that in the first image in this article[1]. The light green band is the most probable event area using LIGO data only. The dark green circle is the combined VIRGO + LIGO data. Note how the LIGO only data can't tell which hemisphere the signal came from, but the addition of the VIRGO data allows them to figure that out.
The blue bands/circle are the optical measurements.
I forgot to add, the reason they don't drill down is because it's hard and expensive. The arms are 4km, and to get the required sensitivity they bounce the light about 300 times before detecting it.
Drilling down 4km would be quite expensive, especially since you need a large mirror assembly[1] and vibration isolation system[2] down there. The mirror assembly and vibration isolation systems would also have to be of a different design, further increasing cost and complexity.
The immediate follow up question would be "but why don't they make the arms shorter?"
As far as I know the problem then is you'd have to bounce the light even more to compensate, and for each bounce you lose some light. Say you drilled "just" 1km down. To compensate you'd have to bounce the light 1200 times. Say the mirrors reflect 99.9% of the light. After 300 bounces you still have 74% of the light left, but after 1200 bounces that's down to 30%. And that's only the reflection loss, then you got beam spread etc.
So why not just increase the laser power to compensate then? AFAIK, increasing laser power means increasing laser noise, so that would ruin your signal to noise ratio.
In addition, the shorter arm means you'll be even less sensitive to longer wavelength gravitational waves, regardless of the number of bounces. The LISA mission was supposed to use satellites flying 2.5 million km from each other, to be able to detect really low frequency waves.
It would be waaaay easier to put additional detector 90 degrees away on the surface of the Earth than it would be to drill 4km into the ground (and service mirrors there!).
Imagine a giant cube around the entire earth that touches in 6 places -- one on each cube face. Pick 3 faces and place a detector where each touches the earth -- on the surface. You can rotate the detectors around on the surface so that you get an arm in each axis relative to the center of the earth.
It can come directly from above, in which case you can't discriminate between from above or from below as it'll hit all arms at the same time if they're at a single location. You'd also have poor directionality.
Wouldn't the Spacetime Cube be just as vulnerable to the perpendicularity problem, though? It might have more sensitivity in near-perpendicular cases, but that's simply because there are more detectors.
"there's a lot of confusion about if space stretches, doesn't that also stretch the light being mesured...
... notice that I didn't say whether space stretches or that time slows down (in response to a passing wave) - since we don't know how exactly space and time are mixed up, we just record that it took longer for the light to come back, but we don't say whether it was a difference in time or a difference in space that cause the slowdown"
"This varying pattern of misaligned laser beams, observed and recorded over the time it takes for the gravitational wave to pass tells us two things: 1. How much the arms changed length during the light-beams' journeys and, 2. the frequency at which, or how quickly the arms changed lengths (longer then shorter then longer, etc.) in response to the gravitational wave. This information can tell us what generated the gravitational wave in the first place.
In this scenario, the actual wavelengths of the beams of light have no bearing on the much more important interference pattern. The effects of the length changes in the arms far outweigh any change in the wavelength of the laser, so we can virtually ignore it altogether."
> Einstein realized that when massive objects such as black holes collide, the impact sends shock waves through space-time that are like the ripples in water created by tossing a pebble in a pond.
What? AFAIK, "like the ripples in water" describes opposite theory.
The visual simile is, of course, not perfect, but the simile is not provided for people that knowledgeable on the science in the first place. If you happen to find a more appropriate simile that people follow, please make it known.
The visual simile is Ok, but it contradicts theory of Relativity developed by Einstein, because theory was based on _absence_ of these ripples in vacuum, as proven by Michelson–Morley_experiment, which leaded to assumption that c(vacuum) = const.
IMHO, author should change text to "like the ripples in fabric of pond created by tossing a pebble in a pond", to be in line with Einstein.
Michaelson-Morley was about a medium in which electromagnetic waves traveled (and in fact proved that it didn't exist). We're dealing with gravitational waves here, which travel... on... space-time itself? But it's not a medium in the sense that the aether was supposed to be.)
At any rate, even the simile doesn't contradict either SR or GR. It's just hard to describe what the waves are traveling on.
In particular, the problem with aether is that it was a non-relativistically-invariant medium (that is, by moving, you could change your speed with respect to the medium). Whatever light and gravity travel in is relativistically invariant, but the waves-in-water analogy for how waves spread is still perfectly appropriate.
Yes, Michaelson-Morley proved that "medium" doesn't exist, because no distortions of speed of light were found. These distortions were found much later by LIGO.
So, IMHO, author should replace "ripples in water" with something scientific, e.g. "ripples of space-time", "ripples of fabric of pond", "excitements of pond field", because now his text makes reader feel like there is water in the pond.
End of trolling.
> In particular, the problem with aether is that it was a non-relativistically-invariant medium (that is, by moving, you could change your speed with respect to the medium).
Yep.
> Whatever light and gravity travel in is relativistically invariant,
LIGO demonstrated that c in vacuum ≠ const, thus they are not.
By the way, medium can change it speed too, it's not a static thing, so theory of relativity can be extended to include medium, which may solve some problems with QM and with experimental observations.
> We're dealing with gravitational waves here, which travel... on... space-time itself?
It's probably easiest to get there by considering the breaking of symmetries of spacetime.
Let's start with the maximally symmetric spacetime: Minkowski spacetime AKA flat spacetime. We can choose any point in the entire spacetime and measure the same field values everywhere. Conventionally we'd normalize the everywhere-and-everywhen-identical measurements to zero.
Let's add a spherically symmetric central mass of uniform density, giving us the Schwarzschild spacetime. This spacetime has two new properties: firstly, there is a location-dependence of the field-values, and secondly the spacetime is asymptotically flat. The gravitational field values will depend on spatial distance from the central mass, and conventionally we normalize so that they will be larger closer to it and smaller further from it. If our central mass emits light, we get the same result: a falling-off of the local intensity of the light with distance, and the "light field" is just the value everywhere of the intensity of the light. At great enough distance, the measurement of gravitational field values is practically indistinguishable from what one would get if measuring Minkowski spacetime anywhere. Likewise, if the object is bright, then at great enough distance we fail to gather up enough light to see the central object: in every direction we look, we see the blackness expected of an empty spacetime. Our field values depend on one particular space-like coordinate; we can vary the other two, or the time-like coordinate, and the field values remain unchanged.
Let's now add a bump on the surface of the sphere, much like a large mountain made up of the same uniformly dense material. Now our gravitational field values will depend on where we measure relative to the bump. The field values at a pair of adjacent points in this spacetime will differ from those we would get in Schwarzchild spacetime. For example, if we see the bump as on the left of the sphere-with-bump then if we measure slightly clockwise or counterclockwise around the object we will see a change in angle reported by a sensitive mass detector that we would not see in the case of the perfectly smooth sphere. If our bump is much brighter than the sphere, and they are both mutually transparent, then we can also tell that the bump is on the left, or behind, or in front of the sphere on which it rests.
This is still an asymptotically flat spacetime: at great distances, our measurements barely register the difference from true Minkowski spacetime. The source of light and gravitation is pointlike at large but closer-in distances so is asymptotically Schwarzschild. Closer in still we begin to register observables that betray the presence of the bump. This is still a time-independent spacetime, though. The field values (gravitational or visual) at a given point are identical at all times; they only differ between points where there is a difference in at least one of the space-like coordinates.
Now let's add some angular momentum, and have the bump be on the equator of the spinning sphere. Now if we choose a point in spacetime, and with a fairly tame choice of coordinates (polar, say, or Cartesian, or their 4-d extensions Schwarzschild coordinates or Minkowski coordinates) if we choose a point in the equatorial plane and hold the three space-like coordinates constant then the field value is time-dependent -- it varies with the angular momentum of the rotating sphere-plus-equatorial-bump.
Let's make the bump bright, and the sphere it sits on dim, and both opaque. Visually, in this time-independent spacetime, if we are in the equatorial plane and not too far away, we will see the bump disappearing behind the bulk of the sphere, then reappearing, brightening as it gets closer, reaching a brightness peak when it closest to us, then dimming prior to its eclipse. If the rotation rate is constant...
It's very good post, except for the fact that you missed the point of discussion completely.
Minkowski space-time is math. Time is used as coordinate. In reality, we cannot walk 10 seconds to the left.
Math is important (major) instrument for physicist, because it's allows us to make predictions for things, which we cannot see with our senses, but here we are talking about nature of the vacuum.
In short, about 100 years ago, the dominant theory was Theory of Ether. Ether was imagined like completely transparent gas or fluid, which transfers light and EM waves like water transfers sound waves.
This theory was replaced by Theory of General Relativity, because ToGR makes much more precious predictions than ToE. The one of the key experiments was Michelson–Morley experiment, which tried to answer is Ether is moves with Earth, so we are moving with our Ether, or is it static, so we are moving trough it at high speed (because of rotation around Sun and around Milki Way center). However, experiment found no disturbances at all, which leads to assumption that there is no medium for EM waves at all.
With time, we have more and more evidence that vacuum is not empty space. (I will use word vacuum instead of Ether, because, like with atom or +/-, it is well-known therm).
1) QM in general. Especially Heisenberg principle of uncertainty. Small particles displays something like Brownian motion: their position is uncertain when they at rest, except that we cannot see that with eyes because, photons are too massive.
2) _Linear_ Sagnac interferometer demonstrates that light is captured with medium, which leads to assumption that physical vacuum is attached to objects like atmosphere is attached to planet. If so, then it's impossible to find distributions of physical vacuum in well isolated room, because vacuum will be still, like air in cabin of airplane. Only major events, like massive explosion, can shake air in the isolated cabin while plan travels through air.
3) Hubble constant is not a constant. It's measured with high precision, but it has different values for different frequencies. If these values are plotted, then they for exponential curve. It's means that light is just ages with distance traveled, i.e. it loses some energy to the medium.
4) LIGO found gravitational waves at 1E-18 precision, which means that Michelson-Morley experiment had much lower accuracy than necessary.
Gravitational waves are disturbances in a background spacetime,
i.e. you linearize the Einstein equations around a given solution.
The analogy is less bad as one might initially think
I attended a conference recently here in India about the Ligo India project. I am on the team that will do the data pipelines for Ligo. The sheer engineering feat makes my software engineering bit like a kindergartener undertaking. Truly massive and impressive.
I'd like to recommend this talk by Daniel Sigg about LIGO [1]. It's technical and explains the design choices that went into building the detector. I found it to be very interesting.
35 comments
[ 2.1 ms ] story [ 67.6 ms ] threadThere are angles where the detector are less effective, but your aim is not to have perfect coverage, it is to detect them.
However, the two detectors that make up LIGO are oriented differently. In addition there's the VIRGO detector in Italy and more detectors being built.
With multiple detectors you can not only measure in different orientations, but also consider the difference in detection time between the detectors. So by combining data you can really narrow it down.
You can see an example of that in the first image in this article[1]. The light green band is the most probable event area using LIGO data only. The dark green circle is the combined VIRGO + LIGO data. Note how the LIGO only data can't tell which hemisphere the signal came from, but the addition of the VIRGO data allows them to figure that out.
The blue bands/circle are the optical measurements.
[1]: http://public.virgo-gw.eu/ligo-and-virgo-make-first-detectio...
Drilling down 4km would be quite expensive, especially since you need a large mirror assembly[1] and vibration isolation system[2] down there. The mirror assembly and vibration isolation systems would also have to be of a different design, further increasing cost and complexity.
[1]: https://twitter.com/ligo/status/601848954645401601
[2]: https://www.ligo.caltech.edu/page/vibration-isolation
As far as I know the problem then is you'd have to bounce the light even more to compensate, and for each bounce you lose some light. Say you drilled "just" 1km down. To compensate you'd have to bounce the light 1200 times. Say the mirrors reflect 99.9% of the light. After 300 bounces you still have 74% of the light left, but after 1200 bounces that's down to 30%. And that's only the reflection loss, then you got beam spread etc.
So why not just increase the laser power to compensate then? AFAIK, increasing laser power means increasing laser noise, so that would ruin your signal to noise ratio.
In addition, the shorter arm means you'll be even less sensitive to longer wavelength gravitational waves, regardless of the number of bounces. The LISA mission was supposed to use satellites flying 2.5 million km from each other, to be able to detect really low frequency waves.
"there's a lot of confusion about if space stretches, doesn't that also stretch the light being mesured...
... notice that I didn't say whether space stretches or that time slows down (in response to a passing wave) - since we don't know how exactly space and time are mixed up, we just record that it took longer for the light to come back, but we don't say whether it was a difference in time or a difference in space that cause the slowdown"
The Technical Challenges of Measuring Gravitational Waves - Rana Adhikari of LIGO https://www.youtube.com/watch?v=1D2j8nTjOZ4
https://www.forbes.com/sites/startswithabang/2018/09/15/ask-...
"Ask Ethan: If Light Contracts And Expands With Space, How Do We Detect Gravitational Waves?"
It also links to the FAQ at LIGO:
https://www.ligo.caltech.edu/page/faq
which for this question ends with:
"This varying pattern of misaligned laser beams, observed and recorded over the time it takes for the gravitational wave to pass tells us two things: 1. How much the arms changed length during the light-beams' journeys and, 2. the frequency at which, or how quickly the arms changed lengths (longer then shorter then longer, etc.) in response to the gravitational wave. This information can tell us what generated the gravitational wave in the first place.
In this scenario, the actual wavelengths of the beams of light have no bearing on the much more important interference pattern. The effects of the length changes in the arms far outweigh any change in the wavelength of the laser, so we can virtually ignore it altogether."
What? AFAIK, "like the ripples in water" describes opposite theory.
The "ripples in water" only refer to the radiation behaving like classical waves, of which water vaves are an example.
IMHO, author should change text to "like the ripples in fabric of pond created by tossing a pebble in a pond", to be in line with Einstein.
At any rate, even the simile doesn't contradict either SR or GR. It's just hard to describe what the waves are traveling on.
In particular, the problem with aether is that it was a non-relativistically-invariant medium (that is, by moving, you could change your speed with respect to the medium). Whatever light and gravity travel in is relativistically invariant, but the waves-in-water analogy for how waves spread is still perfectly appropriate.
So, IMHO, author should replace "ripples in water" with something scientific, e.g. "ripples of space-time", "ripples of fabric of pond", "excitements of pond field", because now his text makes reader feel like there is water in the pond.
End of trolling.
> In particular, the problem with aether is that it was a non-relativistically-invariant medium (that is, by moving, you could change your speed with respect to the medium).
Yep.
> Whatever light and gravity travel in is relativistically invariant,
LIGO demonstrated that c in vacuum ≠ const, thus they are not.
By the way, medium can change it speed too, it's not a static thing, so theory of relativity can be extended to include medium, which may solve some problems with QM and with experimental observations.
It's probably easiest to get there by considering the breaking of symmetries of spacetime.
Let's start with the maximally symmetric spacetime: Minkowski spacetime AKA flat spacetime. We can choose any point in the entire spacetime and measure the same field values everywhere. Conventionally we'd normalize the everywhere-and-everywhen-identical measurements to zero.
Let's add a spherically symmetric central mass of uniform density, giving us the Schwarzschild spacetime. This spacetime has two new properties: firstly, there is a location-dependence of the field-values, and secondly the spacetime is asymptotically flat. The gravitational field values will depend on spatial distance from the central mass, and conventionally we normalize so that they will be larger closer to it and smaller further from it. If our central mass emits light, we get the same result: a falling-off of the local intensity of the light with distance, and the "light field" is just the value everywhere of the intensity of the light. At great enough distance, the measurement of gravitational field values is practically indistinguishable from what one would get if measuring Minkowski spacetime anywhere. Likewise, if the object is bright, then at great enough distance we fail to gather up enough light to see the central object: in every direction we look, we see the blackness expected of an empty spacetime. Our field values depend on one particular space-like coordinate; we can vary the other two, or the time-like coordinate, and the field values remain unchanged.
Let's now add a bump on the surface of the sphere, much like a large mountain made up of the same uniformly dense material. Now our gravitational field values will depend on where we measure relative to the bump. The field values at a pair of adjacent points in this spacetime will differ from those we would get in Schwarzchild spacetime. For example, if we see the bump as on the left of the sphere-with-bump then if we measure slightly clockwise or counterclockwise around the object we will see a change in angle reported by a sensitive mass detector that we would not see in the case of the perfectly smooth sphere. If our bump is much brighter than the sphere, and they are both mutually transparent, then we can also tell that the bump is on the left, or behind, or in front of the sphere on which it rests.
This is still an asymptotically flat spacetime: at great distances, our measurements barely register the difference from true Minkowski spacetime. The source of light and gravitation is pointlike at large but closer-in distances so is asymptotically Schwarzschild. Closer in still we begin to register observables that betray the presence of the bump. This is still a time-independent spacetime, though. The field values (gravitational or visual) at a given point are identical at all times; they only differ between points where there is a difference in at least one of the space-like coordinates.
Now let's add some angular momentum, and have the bump be on the equator of the spinning sphere. Now if we choose a point in spacetime, and with a fairly tame choice of coordinates (polar, say, or Cartesian, or their 4-d extensions Schwarzschild coordinates or Minkowski coordinates) if we choose a point in the equatorial plane and hold the three space-like coordinates constant then the field value is time-dependent -- it varies with the angular momentum of the rotating sphere-plus-equatorial-bump.
Let's make the bump bright, and the sphere it sits on dim, and both opaque. Visually, in this time-independent spacetime, if we are in the equatorial plane and not too far away, we will see the bump disappearing behind the bulk of the sphere, then reappearing, brightening as it gets closer, reaching a brightness peak when it closest to us, then dimming prior to its eclipse. If the rotation rate is constant...
Minkowski space-time is math. Time is used as coordinate. In reality, we cannot walk 10 seconds to the left.
Math is important (major) instrument for physicist, because it's allows us to make predictions for things, which we cannot see with our senses, but here we are talking about nature of the vacuum.
In short, about 100 years ago, the dominant theory was Theory of Ether. Ether was imagined like completely transparent gas or fluid, which transfers light and EM waves like water transfers sound waves.
This theory was replaced by Theory of General Relativity, because ToGR makes much more precious predictions than ToE. The one of the key experiments was Michelson–Morley experiment, which tried to answer is Ether is moves with Earth, so we are moving with our Ether, or is it static, so we are moving trough it at high speed (because of rotation around Sun and around Milki Way center). However, experiment found no disturbances at all, which leads to assumption that there is no medium for EM waves at all.
With time, we have more and more evidence that vacuum is not empty space. (I will use word vacuum instead of Ether, because, like with atom or +/-, it is well-known therm).
1) QM in general. Especially Heisenberg principle of uncertainty. Small particles displays something like Brownian motion: their position is uncertain when they at rest, except that we cannot see that with eyes because, photons are too massive.
2) _Linear_ Sagnac interferometer demonstrates that light is captured with medium, which leads to assumption that physical vacuum is attached to objects like atmosphere is attached to planet. If so, then it's impossible to find distributions of physical vacuum in well isolated room, because vacuum will be still, like air in cabin of airplane. Only major events, like massive explosion, can shake air in the isolated cabin while plan travels through air.
3) Hubble constant is not a constant. It's measured with high precision, but it has different values for different frequencies. If these values are plotted, then they for exponential curve. It's means that light is just ages with distance traveled, i.e. it loses some energy to the medium.
4) LIGO found gravitational waves at 1E-18 precision, which means that Michelson-Morley experiment had much lower accuracy than necessary.
And so on.
https://www.gw-openscience.org/s/events/GW170104/LOSC_Event_...
[1]: https://www.youtube.com/watch?v=j4gE-hSQm68