Natural Sciences

# Ripples in the Cosmos: A Conversation on Gravitational Waves – Part 2

If you’ve just logged on to this conversation, you’re requested to please go through Part 1. In summary, we have the giants who featured in this story of gravitation through the ages in this pan-temporal panel on stage who are asking questions. The central figure is of course Albert Einstein and the panel is chaired by the legendary Carl Sagan. Last we left off after Christiaan Huygens made the suggestion of using light to detect gravitational waves.

Sagan: So, we are back again after the break. Welcome to Part-2. Christiaan Huygens joined us just before the break. So Christiaan, you were saying that we can use light?

Huygens: Yes, of course. You see light is a wave and that is special. It means that light can undergo a special phenomenon called ‘interference’. If you take two light waves and draw the wiggles, you can basically add them up at different points. You can either have constructive interference, when the two light rays add up, or you can have destructive interference when the light rays subtract from each other. You see, here it what it looks like. We didn’t have these things in my days, but now I can even show you a so-called ‘gif’.First a still picture, then a gif.  Isn’t that what they are calling it?

The top curve in bold is the resultant curve of the two waves given below. Note the positions of the highest and lowest points of the two waves and verify that if you added the waves up at every point, you’d get the resultant. This is interference of light.

Interference can give rise to many complicated patterns. Look at two waves originating from the two slits and then adding up. The blue represent a peak while the blank green is just no waves at all. Notice that to the right, near the screen, there are alternate portions showing constructive and destructive interference.

Sagan: I believe so! Maybe, if I made a science series today, I’d have said that in order to make a gif, you first have to invent the Universe.

Huygens: I really haven’t seen your series to get that joke. Anyway, interference of light. Let me explain this in more detail. Let’s say you have two trains of light waves hitting a spot. Now, let one light beam be made to go through a longer optical path. Which basically means it travels an effective distance greater than that through vacuum. Now, if light has to travel this extra distance, it must be going through a different number of waves than the previous wave. Depending on the path length, we can have the two waves either adding up or subtracting from each other. Vary the path length periodically and you’ll have addition and subtraction at the same times.

Sagan: I couldn’t have said that better myself.

Einstein: You know, my special theory was based on the experiment that Michelson-Morley did. They didn’t find anything and that was the clue for me. That was also based on ‘interferometry’, or the technique of making measurements based on interference of light.

Olivia: I understand that you can use light and interference for detecting minor changes in path lengths of two different trains of light waves. But what has that got to do with gravitational waves?

[Enter Lawrence Krauss to great applause]

Sagan: Seems like you rival me in popularity here.

Krauss: I just might, I just might. I’ve been listening to this discussion and it’s been fabulous. Just to answer that last question: suppose a gravitational wave passes through the neighbourhood of these two beams. It may alter one of the beams or both! When these light beams interfere, we can have these interference patterns being set up. Measurement of these patterns can give us details about the perturbation the gravitational waves have caused, which can give us an estimate of the power contained in this gravitational wave.

Carl, if you don’t mind, can I also invite two of my friends, Kip and Stephen?

Sagan: You mean Kip Thorne and Stephen Hawking? I would love them to join us.

Krauss: Great… come on out guys.

[Enter Kip Thorne and Stephen Hawking. Great applause]

Thorne: I don’t know why Lawrence invited us here. I thought he’d be cleaning up the stage here, leaving me free for more important things at home, like a game of cards.

Krauss: I was scared, Kip. Scared that I might give General Relativity so much time and not enough for your baby that people might think that you’ve doing nothing.

Einstein: I wish we had such machinery in my days.

Sagan: So will someone ask the question, or should I ask the most obvious question?

Iago: Me me! What is this LIGO we keep hearing about? How does it work?

Sagan: Good! The young people want to know. Prof. Thorne, I believe that you were one of the people who started with this LIGO experiment, is it not? LIGO stands for Laser Interferometer Gravitational-wave Observatory, by the way. So how does it work?

Thorne: It’s simple really and Lawrence has done a wonderful job explaining its basics. Well, wonderful for a theorist. The whole setup basically consists of two arms placed perpendicularly to each other in an ‘L’ shape. Each arm is 4 km in length, and light can pass through the Fabry-Perot cavities in each of the arms. These increase the path length. Now, 4 km is too short, so we make the light beams go up and down the 4 km slot 75 times. (I have a photo of that.) After this exercise, the two beams are made to meet again at the initial point from there the beam split. There is a measurement unit kept there, a photodiode, and it should measure zero light! That’s the default state of the experiment.

If however, it does detect light, we might have a signal of a gravitational wave passing through the apparatus.

An aerial shot of the LIGO experiment. The perpendicular arms are clearly visible. (Courtesy: LIGO)

Gilbert: Did you guys measure anything till now?

Thorne: We’ve been running LIGO since 2002 but we’ve been completely luckless! We upgraded to Advanced LIGO or aLIGO two years ago and it’s been taking data for a year now. In the coming press release, we report on the progress. And hopefully… maybe…

Krauss: Oh Kip, just tell them that you’ve detected the damned waves! And you’re a theorist too. You co-authored the fattest book on gravitation ever!

Thorne: That’s true, I did write that book! But about LIGO: it’s better to be quiet about these things. We don’t want another BICEP-II.

Iago: Speaking of BICEP-II…

Sagan: We’ll postpone any questions about BICEP-2 till later, after we’ve had replies about LIGO. So any questions?

Lillette: But why has it taken so long to detect the waves?

Hawking: Because the waves are very weak…

Krauss: Yes, exactly as Prof. Hawking mentioned, these gravitational waves are extremely faint! Let me give you an estimate of how faint they are.

Consider the Earth-Sun system. They are orbiting each other and also sending ripples through the space-time fabric – gravitational waves. However, the waves are extremely weak. The power in each of these waves can be estimated to be about 200 watts, which is essentially negligible when you compare it with  roughly $4 \times 10^{26}$ watts of power that the Sun is radiating. Since the Earth-Sun system is radiating energy, the Earth’s orbit is indeed shrinking. But don’t worry, for these gravitational waves, the orbit of the Earth decreases by an average of $10^{-15}$ m, or roughly the diameter of a proton!

That’s extremely hard to detect!

Hawking: Because the waves are very weak…

[Laughter]

Thorne: Adding to what Lawrence said, if a star were to go supernova in a ‘nearby’ galaxy a few million light years away, the gravitational wave produced in that event would squeeze and stretch the two arms of the experiment by $10^{-18}$ m to $10^{-17}$ m , or by only a thousandth to a hundredth of a proton radius!

Hawking: Because the waves are very weak…

Sagan: Prof. Hawking seems to be the keeper of our summary statements.

Iago: So this would go to prove the correctness of Einstein’s theory, right?

Einstein: Ha ha, young people and their enthusiasm.

Krauss: Yes, it would be the most direct proof of the phenomenon of gravitational wave as predicted by Einstein. We already know the theory to be true; this is testing it even further

Hawking: For me, GR is true. It is a measure of our abilities.

Thorne: Thank you, I was just about to say that. While I agree with Lawrence, I think the new LIGO era is a testament to our precision in measurement rather than any verification of General Relativity. We already know the energy loss of different objects and they agree exactly with what the Grand Old Man told us.

Einstein: You do know that I’m sitting right here, right? And please, it’s ‘Einshtein’.

Krauss: I agree with Kip. Not that what I said was wrong, but I understand your point.

There has been interest in a particular type of star system called the Hulse-Taylor binary. It’s basically two neutron stars rotating about each other. (Oh yeah, neutron stars are literally stars made of just neutrons. They are extremely dense objects – the matter is the densest we know of – and they form after supernovas of massive stars.) One of the neutron stars needs to be a pulsar, which basically means that is spinning and radiates. Such pulsars are like lighthouses; their beams can sweep through an area and point at you at specific times. You can time these sweeping beams and they happen to be very regular. Pulsars are natural time-keepers. But, pulsars do slow down, because, of course, they are also in the space-time fabric. They lose energy through gravitational waves.

An illustration of the Hulse-Taylor binary system. (Courtesy: nobelprize.org)

The Hulse-Taylor type stars are perfect as laboratories to test Einstein’s theory. They can lose energy through gravitational radiation and this loss may be significant enough for detection. There is one such system, called the PSR B1913+16 system. The rotation period of the pulsar has been measured very accurately and it’s seen to decrease! But what is astonishing is that…

Einstein: Let me guess, the rate is exactly what you would predict from my theory, isn’t it?

Krauss: Bingo! Let me just show you the curve documenting the rotation time-periods over here –

This is the curve from PSR1913+16 and it shows a clear decrease. The blue curve is the theoretically expected result, according to GR and the red points are observed values. (Courtesy: Wikimedia Commons)

Thorne: Thus my point! General Relativity has been subjected to a gazillion tests and it has withstood all of that. We knew that gravitational waves have to exist, otherwise we would have a problem with the conservation of mass and energy. Existence was never a question, detection was. Now, it finally seems like we are at the doorstep…

Krauss: Is that an admission there?

Thorne: Not at all! No comments.

Krauss:  Should I simply say ‘Woohoo!‘?

Thorne: Nope! You’ll say nothing!

Sagan: Yes, we can have a question about BICEP-II. A quick one!

Iago: Thank you. I just wanted to know what BICEP-II has to do, if at all, with this study. We heard a lot about gravitational waves – how are the two related?

Krauss: Oh, yes we heard a lot about gravitation waves and the B-mode polarization during the BICEP press conference. Unfortunately, it seems like the ‘signal’ wasn’t a signal at all. Well, to answer your question, these gravitational waves, and LIGO in particular, have nothing to do with BICEP-II and what it is measuring. LIGO measures gravitational waves coming from merger of neutron stars. BICEP-II was designed to measure something called B-mode polarization in the Cosmic Microwave Background Radiation. Two very different things. Those B-modes could’ve been set up by primordial gravitational waves, which could’ve originated from inflation, but we just don’t have a measurement for that right now.

Sagan: We’ll end with that wonderful response. Thank you everyone for the wonderful discussion.

Newton: Seems like you guys have come a long way from my days.

Sagan: As I have often said, there is always something wonderful waiting to be discovered somewhere. The bubble of knowledge is always expanding, rather accelerating, just like our own Universe. From the entire panel here, we bid you goodbye. Keep questioning and keep knowing.

Keep watching this space… and time!

There is a lot of popular articles you can read on gravitational waves. You can read the answers provided by the LIGO team in a Reddit AMA thread here or what Prof. Sabine Hossenfelder has to say on this matter in this article on her blog. Happy reading!

UPDATE:-

11th February, 2016: LIGO confirmed that they have indeed detected gravitational waves.

These waves originate from the merger of two blackholes, each with a mass of about 20 solar masses from a region roughly 1.3 billion light years away. The gravitational waves travelled for 1.3 billion years and finally arrived on Earth and produced a signal lasting for 0.2 seconds and producing a change in length of about $10^{-18}$m in a tube of light (one of the arms of LIGO described above) which is 4 km in length. Take a moment let that sink in – $10^{-18}$ metres in a tube which is 4 kilometers in length, or a quarter of $10^{-21}$. It’s like measuring the Earth-Sun distance to the accuracy of a human hair!

The following plot was shown by LIGO and it clearly shows a signal. Take a look at it first and then I’ll explain what’s so remarkable about this:

This shows the signal detected by LIGO. More details in the text. Courtesy: LIGO

LIGO has two detectors – each located on either side of America. They are called LIGO Hanford and LIGO Livingstone, after their locations. On 14th September, 2015, they detected this signal lasting for 0.2 to 0.4 seconds – it’s a measure of strain (as mentioned on the y-axis) versus time. Look at the units of strain on the y-axis! On the first two plots, notice the thin wiggly lines – those are theoretical predictions from Einstein’s General Relativity, the outcome of a lot of hours of computation time and analytical results. Look how well they fit!

Now take a look at the two signals overlapped with each other – remember that these were detected on opposite sides of the American continent! They fit nearly exactly! This isn’t a stray vibration, this is indeed coming from an cosmological source.

“Ladies and gentlemen, we’ve detected gravitational waves. We did it!”

1. LIGO press release: https://www.youtube.com/watch?v=_582rU6neLc   (Very accessible, in case you’re worried)
3. Sean Carroll’s blog: http://www.preposterousuniverse.com/blog/2016/02/11/gravitational-waves-at-last
4. What gravitational waves sound like (yes, you can literally hear them): https://www.youtube.com/watch?v=TWqhUANNFXw

#### Debjyoti

• The LIGO discovery is amazing and a proof of technical virtuosity, but it is more similar to Leverrier’s discovery of Neptune (that simply added a little bit of support to Newton’s theory) than to, for example, Galilei’s telescope discoveries (that helped to discard an established theory and to confirm a new one)

• pannaichan says:

My doubt is whether space/object shrinks due to gravitational wave or the light/laser travels faster due to gravitational wave? If the object/space shrinks, whether it will retain its original shape or permanently shrink/deform after the impact of gravitational wave.

• pannaichan says: