Coronavirus (Covid-19): Latest updates and information
Skip to main content Skip to navigation

Journal Club Week 2 Answers

Follow us on twitter for updates and helpful hints! @physics_journal
B. P. Abbott et al (LIGO Scientific Collaboration and Virgo Collaboration) (2016). Observation of Gravitational Waves from a Binary Black Hole Merger. Physical Review Letters, Vol. 116, No. 061102

Below are some of the best summaries sent in by students across the world. Special congratulations to the students of the Polesworth School, Ellesmore Port C of E College and Queen Elizabeth's Grammar School for having the joint most entries! Well done to all students who submitted their summaries, there were some exceptional answers.

Summaries

1. What makes this such a ground-breaking paper?

The paper reminds us that a struggling patent clerk was able to utilise the tools at his disposal: pen and paper, chalk and board and brainpower to accurately predict the underpinnings of the universe only to be verified over a century later using a $1.1 billion Laser Interferometer Gravitational Wave Observatory equipped with bleeding-edge technology the scientists of Einstein’s time period could only fantasise about. In addition, it provides an entirely new way to observe the mysteries of the cosmos; eagerly awaiting minute ripples in the fabric of space-time created by cataclysmic astronomical events aeons ago to wash over Earth so we may peek back in time to their source.
James


This paper proves the existence of gravitational waves, as predicted by Einstein in 1915 in his general theory of relativity, this is not only ground-breaking as it shows the impressive nature of Einstein’s mind, as he predicted the existence so far in advance to the technology being able to prove his theory. But it is also groundbreaking as it shows an unprecedented feat between a collaboration of hundreds of scientists from across the world to prove the existence of gravitational waves, these are vital to be understood for current theories on the nature of gravity and space-time to be extended even further.
Sophie

2. Without relying on the abstract/conclusion, how would you summarise what you have understood about this paper in one paragraph?

In September 2015 LIGO detected gravitational waves for the first time. Two detectors on opposite sides of the United States, fit with sensors to help minimise environmental disturbances, used test mass mirrors attached to the end of two 4km arms to identify these waves. In space, gravitational waves stretch the fabric of space in one direction and compress it in the perpendicular direction. Using this knowledge, LIGO was designed to measure precise changes in the length of its two arms- when one arm length increased (stretched) and the other length decreased (compressed), the resulting signal indicated gravitational waves. Analysis of the signals allowed scientists to determine more about the nature of the source- the mass and orbital frequency proved that the waves originated from two distant black holes merging into one. Furthermore, the relative arrival times of the signals at the two detector sites determined the position of the source blackhole merger. Searches were then conducted to validate the observations: firstly, a search for any significant changes in the length difference of the detector arms (generic transient search); and secondly, a search to match the observed merger with simulated models (binary coalescence search). This concluded that the chance of these gravitational wave signals being spurious was incredibly low, proving Einstein’s prediction from 1916.

Angelika


On September 14, 2015, gravitational waves (ripples in space-time) were observed directly for the first time which was a ground-breaking discovery. This was the result of the merger of two black holes which went entirely according to Einstein’s predictions. Einstein doubted that these types of waves could ever be detected as they are so minuscule and gravity is the weakest of the four known forces. Einstein’s theory of general relativity matched what LIGO scientists discovered exactly which will enable scientist to study them and learn more. Two large interferometric detectors from LIGO detected the signal known as ‘GW150914’ which can measure length changes caused by gravitational waves. In these, laser light travels along two paths which are split with a semi-transparent mirror. Then the light reaches the end of the paths where the ‘arms’ of the interferometer send the light back as they are mirrors. The two paths of laser light are overlapped at the photodetector. The gravitational waves came from merging two black holes with 29 and 36 solar masses which resulted in a black hole which had a mass of 62 suns. This finding will allow for discovering new types of physics unknown to science with possibilities such as detecting objects further in space.
Katie

3. If you had to explain why someone should read this paper in one sentence, what would you say?

Gravitational waves could open up an entirely new field of astronomy, this paper explains how we are able to detect them through super delicate and huge interferometers, if not only for the confirmation of a cosmic phenomenon predicted by Einstein 100 years ago, then for logistics of the experiment, give this a read.
Tom


In its essence, this paper is an ode to human engineering and the meticulous analysis of evidence; in peering into the darkest events in far-flung corners of our universe, we return triumphant, the tiniest signal proof one hundred years in the making—what could be more momentous?
Acadia

4. Do you have any criticisms of this paper?

Einstein's general theory of relativity states that space and time are both intrinsically linked through the fabric of space-time that makes up our universe. This and the theory of time dilation indicates that gravity affects both the warping of space and time, meaning that gravitational waves would do the same. However, the paper only addresses the warping of space, posing the question of whether the time difference between the arrival of the gravitational wave at Hanford and Livingston is in fact accurate. Granted it can be assumed that since the spatial warping was minute, the impact of the gravitational wave on the local time would also be minimal, but given the magnitude of the speed of light in relation to the distance between the two LIGO observatories, the accuracy of time measurement is vital.
Kitty

Two students went one to do some further investigations and found out some interesting further analysis (and then a subsequent paper disproving the re-analysis!)

The waveform in Fig. 1 is illustrative and not the actual ‘best-fit’ waveform that the LIGO team used in their analysis. This was not made clear in the description of the figure and led to a correlation being seen in the residual noise levels at the Hanford and Livingston detectors, as a fraction of the gravitational wave signal remained in the data. As a result, a Copenhagen team of researchers led by Andrew Jackson suggested that the gravitational wave signal was just the result of a correlated spike in noise at the detectors, for example, a seismic event. The LIGO data and gravitational wave detection have since been confirmed by two independent teams who have also shown that the Copenhagen team handled their data poorly, but the LIGO team should have made it clear that the figure they used was illustrative, or provided a figure of the actual ‘best-fit’ signal they used.
Molly

There has been a paper published in 2017 by Jackson et al. which suggests there is correlation in noise data collected by two LIGO detectors in Hanford and Livingston. As the two detectors are so far apart, there should not be any correlation in the noise data. This indicates that the signal detected has not been completely removed from the background noise, which casts serious doubt on the methods of LIGO’s data analysis. LIGO has also admitted that some of the results published in this paper had been manipulated manually from the original data analysis to be more illustrative, which, unfortunately, was not made clear in the original paper. This further raises questions about the credibility of the results published by LIGO in this paper.

(Sources: https://www.newscientist.com/article/mg24032022-600-exclusive-grave-doubts-over-ligos-discovery-of-gravitational-waves/ and https://arxiv.org/pdf/1706.04191.pdf. There has since been a paper published by an independent group disproving Jackson’s claims and reviving confidence in the results of LIGO.)

Phoebe

The answers to the rest of the questions can be downloaded as a completed Cornell notes template here.

INTRODUCTION

  1. (P1, C1) The ‘linearized weak-field equations’ are simplified versions of the equations from Einstein’s General Theory of Relativity. These equations, amongst other things, describe the working of gravity, space and time. What are some of the solutions (objects or events within the universe) that scientists have found for these equations?
    • Einstein found solutions that were waves.

      Schwarzchild found a solution that turned out to be black holes (actually, the Schwarzchild solution is for a non-rotating, spherically symmetric object. It also describes the space time around the Sun, for example. It describes a black hole if all the mass is contained within a region of radius <2GM/c2, the event horizon).

      Kerr found a solution of rotating black holes (similarly, this is appropriate for a rotating, but otherwise spherically symmetric body, not just a black hole.

  2. (P1, C1) Why should we strictly refer to Einstein’s work as the ‘General Theory of Relativity’ and not the ‘Theory of General Relativity’?
    • Because it is the theory that is general, not the relativity. Einstein came up with two ‘Theories of Relativity’ (these are in essence, theories of motion for when one object moves relative to another). He initially came up with the Special Theory of Relativity, which is special because it is limited to the special case of objects at constant velocity. The General Theory of Relativity broadens his previous work and applies also to accelerating objects (and hence objects experiencing a gravitational attraction), and those whose accelerations are also variable.

  3. (P1, C1) What is a black hole? And what is a black hole merger?
    • A black hole is a region of spacetime where the gravitational field is so strong that neither particles nor light can escape it (hence named ‘black’ as light cannot get out). It’s often thought of as a region of unimaginably compact mass (high density), but this depends on how you consider the size of the black hole. Certainly, at its centre – a region known as the singularity of a black hole – the density is infinite. But if we consider the size of the black hole to be the region enclosed by the event horizon (the boundary within which nothing can escape), then the density is actually comparable to many earthly objects. For example, supermassive black holes have an average density similar to water if we consider their volume to be the volume contained within the event horizon. Black holes can form at the end of the life of stars (so-called Stellar Black Holes and it’s hypothesised that some formed in the very early universe (so-called Primordial Black Holes). A black hole merger is when two black holes collide together to form a larger black hole. They don’t collide head on, but orbit around their mutual centre of mass, orbiting one another faster and faster until they eventually come together. The important point here is that they only come together because they emit gravitational waves. The gravitational waves carry energy and angular momentum from the orbit and cause the merger.

  4. (P1, C1) Gravitational waves can be described as ‘transverse waves of spatial strain’ - what does this mean?
    • The gravitational waves are transverse waves (the oscillation is perpendicular to the direction of travel) and the oscillation is one of a strain (a change in length) in space itself. Space (and time!) is squeezed and stretched with the passing of a gravitational wave.

  5. (P1, C1) How have black holes been detected previously?
    • Through ‘electromagnetic observations’ - looking at the radiation (from any part of the electromagnetic spectrum) that is emitted by matter close to the black hole (but not by the black hole itself, as they don’t emit radiation by definition). The most solid evidence for stellar-mass black holes comes from binary stars where we can use the properties of the orbit of the companion star that feeds the black hole to infer the black hole mass.

  6. (P1, C2) Given that Hulse, Taylor and Weisberg have shown the existence of gravitational waves from their analysis of a binary pulsar system (binary means two, a pulsar is a spinning neutron star that emits electromagnetic radiation from its poles), why are the findings of this paper considered to be ground-breaking? (This link gives some detail on the Hulse-Taylor binary that won them a Nobel prize https://en.wikipedia.org/wiki/Hulse–Taylor_binary)
    • This paper is the first direct observation of gravitational waves. Hulse, Taylor and Weisberg could only make sense of their observations of the two pulsars by including energy that was being emitted from the system as gravitational waves, but they didn’t actually detect the gravitational waves. The movement of the two stars implied the existence of gravitational waves, in the same way that seeing a boat move up and down on the ocean implies the existence of waves in the ocean. But they didn’t actually see the waves themselves.

  7. (P1, C2) What are some of the detectors that have previously hunted for gravitational waves unsuccessfully?
    • Weber’s resonant mass detectors, cryogenic resonant detectors, interferometric detectors (that were suggested in the 1960s and 1970s) before being tested and finally built in the early 2000s (e.g. TAMA 300, GEO 600 and LIGO).

  8. (P1, C2) What characteristic makes Advanced LIGO (which is the improved version of LIGO) the only detector to have directly seen gravitational waves?
    • It has a much greater sensitivity for detecting variations in length (and hence variations in space itself). Despite the huge mass energy densities involved in the merger, at our distance the amplitude of the wave (as expressed by strain) is incredibly tiny, thus it took a century to actually measure them.

  9. (P1, C2 and P2, C1) Why are ‘highly disturbed black holes’ such vital objects for testing the predictions of the General Theory of Relativity?
    • Because these highly disturbed black holes (e.g. black hole mergers) are events of extremely high gravitational fields and significantly high velocities and accelerations – they are therefore testing the regime of the General Theory of Relativity, which only makes unique predictions that Newton’s theory of gravity would not include, at these very high accelerations and gravities. However, there are two factors that make testing the General Theory of Relativity quite hard. First gravity is a very weak force, just think it takes the entire mass of the Earth to cause a book to fall down to the ground, and even a child is strong enough to pick it back up and counter that force. The waves in spacetime caused by gravity are incredibly small for even objects as massive as the Sun. Second, the objects which do have gravity strong enough to test the predictions of the General Theory of Relativity are very far away, millions of light years in this case. This is why only the most massive and gravitationally intense events are going to be strong enough to be detected here on Earth, and even then, we require some of the most sensitive equipment scientists have ever made.

DETECTORS (You might find some helpful additional information at https://www.ligo.caltech.edu/page/ligos-ifo for this section)

  1. (P3, C1) Why do they need multiple detectors that are widely separated?
    • So that they can tell apart gravitational wave signals from other sources of vibration that occur locally. Also having two detectors allows the direction of the wave to be found, in the same way that having two ears allows us to hear the direction of sounds, because there is a slight difference in the time when each detector receives a signal.

  2. (P3, C1) Give an example of the type of environmental noise that can be isolated by having detectors separated by large distances?
    • Earthquakes, cars, building work, animals digging burrows. Anything that could disturb the ground locally. Particularly concerning are things which happen at the same frequency as the gravitational waves. The detectors operate from ~10-1000 Hz. Seismic noise dominates the low end frequency sensitivity.

  3. (P3, C1&C2) Each Advanced LIGO experiment consists of “a modified Michelson interferometer that measures gravitational-wave strain as a difference in length of its orthogonal arms”. Using the diagram in Figure 3, explain this in simple terms.
    • Advanced LIGO consists of two arms that are at 90 degrees to one another (orthogonal). It operates using the principle of interference – that waves can be combined in a constructive (additive) or destructive (depletive) manner. The two arms of Advanced LIGO work as a Michelson interferometer whereby the light from a laser, which is all in phase with itself at the start, is split by a beam splitter into the two arms. Light travels along each arm and is then reflected by a mirror so that it travels back along each arm. The light recombines to form an interference pattern depending upon the amount of path difference between the two paths. More specifically, LIGO detectors destructively interfere the waves so that the detectors sit in the dark. When the gravitational waves pass through they change the path length so the cancellation is no longer perfect and there are repeating flashes of light from the passage of the gravitational wave. There are a few hundred photons from this particular gravitational wave source. Even a tiny path difference will cause some interference to be seen.

  4. (P3, C2) When a gravitational wave passes through the equipment, what does it do to the arms? How does Advanced LIGO notice such a difference?
    • Changes the length of one arm relative to the other. As a gravitational wave changes space itself, if the wave hits the arms in the right way then the path that the light has taken will be lengthened or shortened in one of the arms compared to the other. As there is a path difference between the light travelling in each arm if a gravitational wave passes through, then once the light is recombined prior to the detector, the interference pattern will have altered.

  5. (P3, C2) Advanced LIGO gives its measurements in terms of strain (which LIGO give the symbol, h), which is defined as the change in length (ΔL) divided by the total length (L). So the equation is h=ΔL÷L. Why is strain unitless?
    • Because it is defined as a length divided by another length. Both of these have the same units and so once divided, the result is unitless (or, more formally, dimensionless).

  6. (P3, C2) Using the equation from strain (h=ΔL÷L), if the total length of one of the arms is 4 km, and the maximum strain measured by Advanced LIGO (according to the abstract) is 1.0×10-21, then what is the maximum change in the length of one of the arms?
    • If h= 1.0x10-21, and L=4km=4000m, then ΔL=h×L so

      ΔL= 1.0x10-21×4000=4 x10-18m. This is just larger than the purported size of quarks (these sizes aren’t confirmed) and are smaller than the sizes of single protons or neutrons.

  7. (P3, C2) Advanced LIGO is not a basic Michelson interferometer, what have they done to enhance the signal?
    • By having two mirrors in each arm (one at each end), the light actually traverses the ‘resonant cavity’ that is formed by letting the light bounce between the mirrors 4km apart, 300 times. This increases the distance that the light travels to 1200km. To achieve this number of reflections, you need lots of laser power to counteract the very small losses at the optical (mirror) surfaces.

  8. (P4, C1) The laser that they use is ‘a 1064-nm wavelength Nd:YAG laser, stabilized in amplitude, frequency, and beam geometry’. In what region of the electromagnetic spectrum is the laser and why does it need to be stabilised?
    • 1064nm (1.064µm) is in the infrared part of the electromagnetic spectrum. It needs to be stabilised to ensure that, when the light is recombined, any interference is due to gravitational waves causing space to change, not because the light varied a little in its frequency due to the source.

  9. (P4, C1&C2 and P5, C1) What are some of the ways in which the equipment has been built so as to minimise vibrations that would alter the positions of the mirrors?
    • The mirrors are supported in a quadruple pendulum system to damp their movement from the outside world, as well as being put on an active seismic isolation platform. Materials are chosen to reduce mechanical loss throughout. Further vibration isolation stages and ultrahigh vacuums are used. A neat analogy for the “active seismic-isolation platform” is that it works just like noise cancelling headphones, by moving the mirrors in such a way as to cancel the effects of seismic noise.

  10. (P4, C1&C2 and P5, C1) What are some of the ways in which the equipment has been built so as to monitor vibrations that would alter the positions of the mirrors?
    • They monitor the change in position of the mirror caused by the laser itself as the collision between photons and the mirror imparts momentum to the mirror, moving it by a small amount. They monitor this by comparing to a calibration laser. The also use simulated waveforms to check the calibration of the detector. They monitor environmental disturbances with seismometers, accelerometers, microphones, magnetometers, radio receivers, weather sensors, ac-power line monitors, and a cosmic-ray detector.

  11. (P5, C1) One of the key aspects of Advanced LIGO is having the two sites at opposite sides of the United States (see Figure 3a). It takes light 10 ms to travel directly between these sites (and as gravitational waves travel at the speed of light as well, this is true of gravitational waves too). Advanced LIGO is therefore looking for a similar signal at both sites but shifted in time by a small amount. How do they ensure their timings are accurate to know that any gravitational wave has travelled at the speed of light between the two stations?
    • They synchronise their timings to GPS (to better than 10µs). They have an atomic clock and a second GPS receiver to verify timings.

  12. (P4) Figure 3(b) shows a graph of the noise experienced at each of the Advanced LIGO sites around the time of the detection. Discuss what you see in this graph (remember that is uses log scales).
    • There is a general trend at both sites that the strain noise decreases from around 10-22 at 20Hz down to 8×10-24 at 200Hz (remember the log scales used). The amount of noise then increases again to around 3×10-23 at 2000Hz. The noise at both sites follows this general trend. On top of this, there are peaks in the distribution throughout, that can reach up to around 2×10-21. Some of these are common to both sites, though not all. The sources of some of these features are discussed in the caption.

DETECTOR VALIDATION

  1. (P5, C1&2) This section discusses the checks they performed to ensure their signal wasn’t spurious. Given that the answer is “no, we didn’t find anything”, why is such a section necessary?
    • To show their scientific integrity. The scientific community want to be sure that this observation is a true observation so it’s important for the researches to list all the checks they did complete in case anyone else thinks of something they’ve missed. Scientists aren’t just reading this thinking “I’m sure this is correct”, they often spend their time thinking “I wonder if this might be wrong”. This section is written to allay some people’s fears about the origins of their signal.

We now go backwards in the paper to the section on OBSERVATION

III. OBSERVATION

  1. (P2, Figure 1) Looking at the top left panel of the figure (the observed Hanford, Washington signal), describe the signal (you may find it useful to look at the panel beneath it too – a simulation of a gravitational wave event that they believe would match their signal).
    • We see something that initially looks a like noise from 0.25-0.325s. Around 0.325s a wave seems to appear in the data, oscillating around a strain of 0.0. The wave increases in frequency and amplitude up to around 0.425s where it reaches a maximum strain of around ±1×10-21 (which is what we knew from the abstract). After 0.425s, the amplitude then rapidly decreases.

  2. (P2, Figure 1) In the top right panel, they show the data from the Livington, Louisiana site with the Hanford, Washington data added to it but shifted and inverted. It is rare in science to simply shift and invert your data to show that they agree. Reading the caption, why is it necessary to perform this shift and inversion (and in fact also an important sanity check on their results)?
    • The data must be shifted in time to account for the distance between the detectors and the fact that it takes time for the gravitational wave to pass from one to the other. The signal must be inverted as the orientations of the L-shaped interferometers are not the same at both sites.

  3. (P2, Figure 1) In the third row of the Figure, we see the residuals. These are the result of subtracting the simulated data (the data in the second row) from the real data (the data in the top row). These residuals seem to show nothing but noise, why is this a good thing?
    • It means that all of the pertinent features of the measured signal and the simulated signal are in agreement. If the theory and the data did not match, then when they are subtracted, you’d be left with a residual that still had significant features in it. Here, though, the residual seems to be just noise, centred on 0.0 as you would hope.

  4. (P3, C1) Other than to distinguish between signal and noise, why else do they have two detectors on opposite sides of the country?
    • To be able to tell where in the sky the gravitational wave originates from. Much like triangulation of phone signal data, the time delay between the signal’s arrival at the two sites combined with the knowledge that gravitational waves travel at the speed of light allows us to work out a rough area of the sky the gravitational waves originate.

  5. (P3, C1) What general method do researchers use to understand what astronomical objects are the cause of the gravitational waves?
    • They compare to computer simulated models using the simplified Einstein equations, of all sorts of different astronomical events to see which closely matches the observed signal. In this case, the increase in frequency and amplitude, combined with the sudden ‘ring-down’ (where the amplitude rapidly decreases) is indicative of two black holes orbiting closer before combining.

  6. (P3, C1) Why does the emission of gravitational waves cause two black holes to orbit closer?
    • Because the emission of gravitational waves leads to energy loss from the system of the two black holes. As the black holes become less energetic, the strong gravitational attraction between the black holes can bring them closer and closer together.

  7. (P3, C1) Why can the signal not be due to two neutron stars colliding?
    • Due to the smaller masses of neutron stars (compared to black holes), they orbit one another at significantly higher frequencies than those measured in the lead up to the merger.

  8. (P3, C1) Why can the signal not be due to a neutron star and a black hole colliding?
    • A black hole and neutron star that could give rise to the correct ‘chirp mass’ would need very a very large total mass. If this was the case, they’d merge at a lower frequency.

  9. (P3, C1) Why can the signal not be due to other astronomical objects colliding?
    • Neutron stars and black holes are the astronomical objects which are the densest. To reach the orbital frequency observed (75Hz), the objects must be able to get very close to one another (to complete orbits) prior to merging. This requires the objects to be small. We know that to cause such significant gravitational waves, the objects must have a very large mass. Therefore, the conclusion is that the objects must be very dense, leaving us with just neutron stars and black holes as the possible causes.

  10. (P3, Figure 2) At the top of the panel, there are 4 diagrams. Describe what is happening in these diagrams and how it relates to the numerical simulation of the strain (the red line).
    • We have two objects orbiting one another. The inspiral is when the objects get closer and closer together whilst still orbiting one another. As they orbit closer and closer, the frequency of the gravitational waves emitted increases (which we would see as the strain – the change in length seen on earth - changing more rapidly). Just prior to the merger, the gravitational waves are at their maximum frequency as the objects are orbiting as frequently as possible so the strain changes most rapidly here. The increase in amplitude of the gravitational waves is caused by the objects being closer together, so that the gravitational force is even stronger and so shedding even more energy as gravitational waves. Once merged, the objects now form one single object, whose mass is no longer in a state of great change – this means that the gravitational waves stop very suddenly after the merger.

  11. (P3, C1) Looking at the equation for the chirp mass, validate that units remain kg in each part (the f with a dot above it is the time derivative of frequency and so has units of s-2).

Now we move to section V. SEARCHES

V. SEARCHES

  1. (P5-P7) We don’t know beforehand when a gravitational wave event is going to happen. How does this affect the way in which we attempt to measure such events?
    • Scientists have to measure over a long period of time and then analyse all of the data to see if an event occurred at any point in their data. Given that they have so much data, they need ways to search it to isolate what is signal and what is noise. These searches take two forms here, one where they look for any signals whatsoever and quantify how significant it is (taking into account they have two sites and are looking for coincident data). The other search takes theoretical models of what the data could look like in different scenarios and compares it to the measured data to see if it fits and explains where their signal came from.

  2. (P6, Figure) What would you say is the key message to understand from this figure about the event GW150914?
    • That the GW150914 event stands alone in a very statistically significant portion of the picture. Unlike other events, it is far away from the lines that mark what the random background noise events look like, showing it to be something significant.

  3. (P7, C1) Why is the mass of the merged black hole less than the mass of the two initial black holes combined?
    • Because, as the two black holes go through the process of merging, they lose energy in the form of gravitational waves. As energy and mass are interchangeable from Einstein’s relation (E=mc2), any energy that has been lost to the universe from the two black holes will not be held in the mass of the final, merged black hole.

SUMMARY QUESTIONS

  1. What makes this such a ground-breaking paper?
  2. Without relying on the abstract/conclusion, how would you summarise what you have understood about this paper in one paragraph?
  3. If you had to explain why someone should read this paper in one sentence, what would you say?
  4. Do you have any criticisms of this paper?

OPTIONAL EXTRA

Professor Andrew Levan has written an amazing worksheet to teach you how to perform calculations in the programming language, Python. You’ll be initially calculating gravitational forces and then applying this to the study of gravitational waves from compact binary systems. You could perform these calculations on an online Python emulator such as this.

GENERAL INFORMATION

Remember, reading a paper isn't like reading a piece of fiction or a newspaper article. Don't get frustrated if it doesn't immediately make sense - you might need to do a little research of your own to understand some of the ideas. This article gives you an idea of how scientists read differently.

Each question refers to a specific part of the paper e.g. Page 2, Column 3 is written as (P2, C3).

Next week, we'll publish solutions to the questions and the best submitted summaries from students across the country.

NEXT WEEK

We're going to be looking at what some scientists are getting up to in isolation at home with a group trying to solve the puzzle of room temperature superconductivity. As a bit of background, you could watch this summary of why superconductors might be useful to us. This page outlines some of the history of superconductivity (with lots of links throughout and down the sidebar) and highlights some of the research being undertaken within our University.