# Gravitational wave distortion

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Gravitational waves detected are from merging of black holes few millions of light years away. While waves have reached us after travelling so far, they must have encountered many black-holes and have reached us after refracting/gravitational lens effects. Then how do one decide the correct direction of those merging black holes?

Gravitational waves detected by the LIGO that originate a few million light years away is not far away, relatively speaking, at all. As user Chappo has noted, space is mostly empty. Although gravitational waves can be scattered or distorted by an sufficiently massive and dense celestial body, it has a very low probability of happening. Although the technology today has no way of determining the original position of where the waves originate if the waves are disturbed, such disturbance is very unlikely. So it is safe to say that almost all waves detected by the LIGO can be traced back to their original positions.

Gravitational waves are affected by gravitational lensing in the same way as light. Most lensing events are not caused by black holes, but by more common objects with similar mass.

There largest deflection examples of the light from distant galaxies, quasars etc being diverted by foreground sources (clusters of galaxies) is about an arcminute (e.g. Zitrin et al. 2014). Current gravitational wave detectors are not capable of locating sources even to a few degrees. So source location isn't an issue at present.

Source strength might be. A lensed source can be magnified or even split into multiple images that arrive at different times. This will lead to a luminosity distance underestimate from a gravitational wave source and an overestimate of its mass.

For those that are interested, Oguri et al. (2018) have done an extensive set of simulations, showing the effects of gravitational lensing on estimates of mass and redshift distributions for black hole binary gravitational wave sources.

The conclusion is that for detectors like LIGO there should be a (very) small tail of highly magnified events with underestimated redshifts and overestimated masses. These are predominantly at (chirp) masses $$>40 M_{odot}$$ (which is also roughly the minimum mass of the primary component in a binary) and more massive than any of the LIGO events seen so far.

The "optical depth" to lensing as a function of source redshift is shown in Fig. 3 of that paper. What this shows is that the chance of any individual source being strongly ($$>$$ factor of 10 or split into multiple images) lensed is less than one in a million at typical LIGO source distances of a billion light years (redshifts of less than 0.1). But this probability can increase by several orders of magnitude at the high redshifts that might be probed by detectors in the future.

## Brief Introduction Of Gravitational Waves

Gravitational waves are 'ripples' in space-time caused by some of the most violent and energetic processes in the Universe. Albert Einstein predicted the existence of gravitational waves in 1916 in his general theory of relativity. Einstein's mathematics showed that massive accelerating objects (such as neutron stars or black holes orbiting each other) would disrupt space-time in such a way that 'waves' of undulating space-time would propagate in all directions away from the source.

These cosmic ripples would travel at the speed of light, carrying with them information about their origins, as well as clues to the nature of gravity itself. In gravitational-wave astronomy, observations of gravitational waves are used to infer data about the sources of gravitational waves. Sources that can be studied this way include binary star systems composed of white dwarfs, neutron stars, and black holes and events such as supernovae, and the formation of the early universe shortly after the Big Bang.

### Sources Of Gravitational Waves

• Binaries
• Black hole binaries
• Supernovae
• Spinning neutron stars
• Inflation

### What Happens When GW Passes US

Gravitational waves are constantly passing Earth however, even the strongest have a minuscule effect and their sources are generally at a great distance. For example, the waves given off by the cataclysmic final merger of GW150914 reached Earth after travelling over a billion light-years, as a ripple in spacetime that changed the length of a 4 km LIGO arm by a thousandth of the width of a proton, proportionally equivalent to changing the distance to the nearest star outside the Solar System by one hair's width.

## 1. The First Black Holes

In some ways, black holes are simple objects. Whenever a spot in the universe ends up with more mass than it can handle, it may form a singularity — a point of near-infinite density where the usual rules of physics break down. Nothing that gets too close, including passing light, can elude its gravitational pull. At the center of every black hole, astronomers believe, a singularity of this sort resides.

The oldest known black hole appeared more than 13 billion years ago, about 690 million years after the Big Bang, but the first ones could have materialized much earlier: within a fraction of a second of the Big Bang. (Theorists think they might have formed when high-density regions in the turbulent newborn universe collapsed.)

Assuming they exist, these so-called primordial black holes would be different from the most common variety, which form when a massive star exhausts its nuclear fuel and can no longer withstand its own gravity. As a result, while normal “stellar” black holes are considered well-established features of the universe, primordial black holes have remained hypothetical and mysterious for half a century. But a new technique, relying on gravitational waves, may reveal their presence.

Astrophysicists Savvas Koushiappas of Brown University and Avi Loeb of Harvard University have devised a simple way to search for primordial black holes. It revolves around searching for gravitational ripples caused by ancient black holes colliding, the best means of detecting them today.

Primordial black holes were first proposed in 1966 by Russian scientists Yakov Zeldovich and Igor Novikov. Stephen Hawking developed the idea further about five years later. Researchers have been looking for evidence of primordial black holes ever since.

The duo started by reasoning that in the very early universe, primordial black holes were the only kind possible, since star-based black holes can’t form before stars themselves. So, they estimated the earliest possible time a pair of stellar black holes could possibly have crashed together, reasoning that any gravitational ripples seen before then must have been caused by primordial black holes. Based on conservative assumptions, they found that the first stellar black holes could not have formed and crashed until at least 67 million years after the Big Bang.

So if LIGO sees waves from black hole mergers taking place before that cutoff, it would mean one of two things: The first and most exciting possibility is that primordial black holes really do exist, thus confirming a long-standing conjecture. As a bonus, Koushiappas and Loeb have determined that primordial black holes could make up some of the universe’s still-unexplained dark matter, so the finding could offer a partial solution to one of astronomy’s biggest mysteries.

The second interpretation is simply that the standard cosmological picture is somehow amiss. “Either way,” says Loeb, “it would be big news, telling us there’s some new physics here that we don’t fully grasp.”

## Straight Out of the Big Bang: New Type of Gravitational Wave Detector to Find Tennis Ball-Sized Black Holes

“Detecting primordial black holes opens up new perspectives to understand the origin of the Universe, because these still hypothetical black holes are supposed to have formed just a few tiny fractions of a second after the Big Bang. Their study is of great interest for research in theoretical physics and cosmology, because they could notably explain the origin of dark matter in the Universe.” You can see stars in the eyes of the members of the team led by Professor Fuzfa, astrophysicist at UNamur, when talking about the perspectives of their research. This project is the result of an unprecedented collaboration between the UNamur and ULB, to which the ENS added thanks to the involvement of trainee student Léonard Lehoucq.

The idea was to combine the UNamur expertise in the field of gravitational wave antennas, an idea patented by Professor Fuzfa in 2018 and studied by Nicolas Herman as part of his doctorate, with that of ULB in the booming field of primordial black holes, in which Professor Clesse is one of the central players. They have just developed an application of this type of detector in order to observe “small” primordial black holes. Their results have just been published in the journal Physical Review D. “To this day, these primordial black holes are still hypothetical, because it is difficult to make the difference between a black hole resulting from the implosion of a star core and a primordial black hole. Being able to observe smaller black holes, the mass of a planet but a few centimeters in size, would make the difference,” the team of researchers says. They carry on: “We are offering experimenters a device that could detect them, by capturing the gravitational waves they emit when merging and which are of much higher frequencies than those currently available.”

But what is the technique? A gravitational wave “antenna,” composed of a specific metal cavity and suitably immersed in a strong external magnetic field. When the gravitational wave goes through the magnetic field, it generates electromagnetic waves in the cavity. In a way, the gravitational wave makes the cavity “hiss” (resonate), not with sound but with microwaves.

This type of device, just a few meters in size, would be enough to detect fusions of primordial small black holes millions of light years from Earth. It is much more compact than the commonly used detectors (LIGO, Virgo and KAGRA interferometers) which are several kilometers long. The detection method makes it sensitive to very high frequency gravitational waves (in the order of 100 MHz, compared to 10-1000 Hz for LIGO / Virgo / Kagra), which are not produced by ordinary astrophysical sources such as fusions, neutron stars or stellar black holes.

On the other hand, it is ideal for the detection of small black holes, the mass of a planet and its size goes from a small ball to a tennis ball. “Our detector proposal combines well mastered and everyday life technologies such as magnetrons in microwave ovens, MRI magnets and radio antennas. But don’t take your household appliances apart right away to start the adventure: read our article first, then order your equipment, understand the device and the signal that awaits you at the output,” the researchers say laughingly.

This patented technique is currently at the stage of advanced theoretical modeling, but has all the necessary elements to enter a more concrete phase, with the construction of a prototype. In any case, it paves the way for fundamental research into the origins of our Universe. In addition to primordial black holes, this type of detector could also directly observe the gravitational waves emitted at the time of the Big Bang, and thus probe physics at much higher energies than the ones achieved in particle accelerators.

## Finding NEMO: The future of gravitational-wave astronomy

Recent transformational discoveries are only the tip of the iceberg of what the new field of gravitational-wave astronomy could potentially achieve.Credit: Carl Knox/OzGrav/Swinburne

A new study released today makes a compelling case for the development of "NEMO"—a new observatory in Australia that could deliver on some of the most exciting gravitational-wave science next-generation detectors have to offer, but at a fraction of the cost.

The study, co-authored by the ARC Center of Excellence for Gravitational Wave Discovery (OzGrav), coincides with an Astronomy Decadal Plan mid-term review by Australian Academy of Sciences where "NEMO" is identified as a priority goal.

"Gravitational-wave astronomy is reshaping our understanding of the universe," said one of the study's lead authors ARC Future Fellow, Dr. Paul Lasky, from the Monash University School of Physics and Astronomy, and OzGrav.

"Neutron stars are an end state of stellar evolution," he said.

"They consist of the densest observable matter in the universe, and are believed to consist of a superfluid, superconducting core of matter at supranuclear densities. Such conditions are impossible to produce in the laboratory, and theoretical modeling of the matter requires extrapolation by many orders of magnitude beyond the point where nuclear physics is well understood."

The study today presents the design concept and science case for a Neutron Star Extreme Matter Observatory (NEMO): a gravitational-wave interferometer optimized to study nuclear physics with merging neutron stars.

The concept uses high circulating laser power, quantum squeezing and a detector topology specially designed to achieve the high frequency sensitivity necessary to probe nuclear matter using gravitational waves.

The study acknowledges that third-generation observatories require substantial, global financial investment and significant technological development over many years.

According to Monash Ph.D. candidate Francisco Hernandez Vivanco, who also worked on the study, the recent transformational discoveries were only the tip of the iceberg of what the new field of gravitational-wave astronomy could potentially achieve.

"To reach its full potential, new detectors with greater sensitivity are required," Francisco said.

"The global community of gravitational-wave scientists is currently designing the so called 'third-generation gravitational-wave detectors (we are currently in the second generation of detectors the first generation were the prototypes that got us where we are today)."

Third-generation detectors will increase the sensitivity achieved by a factor of 10, detecting every black hole merger throughout the universe, and most of the neutron star collisions.

But they have a hefty price tag. At about $1B, they require truly global investment, and are not anticipated to start detecting ripples of gravity until 2035 at the earliest. In contrast, NEMO would require a budget of only$50 to \$100M, a considerably shorter timescale for development, and it would provide a test-bed facility for technology development for third-generation instruments.

The paper today concludes that further design studies are required detailing specifics of the instrument, as well as a possible scoping study to find an appropriate location for the observatory, a project known as "Finding NEMO."

The Laser Interferometer Gravitational-wave Observatory (LIGO) detectors are designed to sense the orthogonal stretching and squeezing of spacetime produced by gravitational waves. Input laser light is split by a beam splitter so that 50% of the light travels down each of two orthogonal 4 kilometer long arms. Any relative change in length between the two perpendicular arms induced by passing gravitational waves will cause an interference pattern in the light that is read out at the output port.

We can directly sense the relative change in length between the interferometer arms as a time series.

The twin LIGO gravitational wave detectors are located in Livingston, Louisiana and Hanford, Washington. There are currently two LIGO detectors in the U.S., with another LIGO detector planned to be built in India.

The LIGO interferometers are the most precise measurement devices ever constructed. The video below shows the measurement of the relative change in length between the 4 kilometer long orthogonal interferometer arms to scale. The LIGO instruments can sense changes in length up to 10,000 times smaller than the width of a proton. This is equivalent to sensing a change in length the width of a human hair between the Earth and the nearest star system, Alpha Centauri.

## The Future of the Search for a Gravitational-Wave Background

For decades, scientists have used networks of pulsars to search for a faint, background gravitational-wave signal that should pervade our universe. What have they found so far, and what can we expect in the future? A new publication details the possibilities.

#### Humming in the Background

Mrk 739 is an example of a galaxy merger where the two nuclei at the center of the newly-formed galaxy are still in the process of merging. [SDSS]

When galaxies collide, the supermassive black holes at their centers should also form binaries, inspiral, and merge. The combination of all inspiraling supermassive black hole binaries across the universe should produce a deep background hum of gravitational waves — a signal that we could detect, with the right tool. Enter: pulsar timing arrays (PTAs).

#### Cosmic Clocks

PTAs rely on the remarkably consistent timing of flashes of light from a network of spinning neutron stars — pulsars — to measure the stretching of the spacetime in which these pulsars are embedded.

An artist’s illustration showing how a network of pulsars could be used to search for the ripples in space-time. [David Champion/NASA/JPL]

#### A Hint of a Signal

How are PTAs doing so far? The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has been searching for the gravitational-wave background for more than a decade — until now, without success. But the longer we observe the timings of a set of pulsars, the more subtle a signal we can detect.

The 12.5-year dataset released this year offers a first glimpse of hope: this most sensitive dataset yet shows signs of a signal consistent with the predicted gravitational-wave background. Definitive evidence of the background will require longer observations with NANOGrav to beat down the noise and reveal an expected set of correlations between pairs of pulsars.

The gravitational wave spectrum and detectors. Here, frequency of the gravitational waves is plotted against strain (the fractional change in the separation between objects caused by the passage of the gravitational wave). Click to enlarge. [NANOGrav]

Pol and collaborators identify three key milestones that we should soon achieve.

1. Robust evidence of the gravitational-wave background should be possible with 15–17 years of data — only another 2–5 years beyond the 12.5-year dataset already published.
2. The signal detected at this time will already contain enough information to identify whether the gravitational-wave background is caused by supermassive black hole binaries, as anticipated, or if it instead has more exotic origins, like primordial black holes or cosmic strings.
3. If the signal is caused by supermassive black holes, the initial detection will also be sufficient to distinguish between different population models for supermassive black hole binaries.

This work illustrates that NANOGrav has the potential to provide us with a wealth of information in the next few years! What’s more, those results will come even faster with the addition of new pulsars to NANOGrav’s network, or the combination of data from multiple PTAs. Gravitational-wave astronomy is truly only just getting started!

Top: Evolution of the signal-to-noise ratio as a function of time observing the pulsars. Middle: The predicted correlation signal between pulsars after 12 years, 15 years, and 20 years, compared to the model (dashed red line) showing the presence of a gravitational-wave background. Bottom: The signal-to-noise ratio of the correlation signal as a function of observing time. [Pol et al. 2021]

#### Citation

“Astrophysics Milestones for Pulsar Timing Array Gravitational-wave Detection,” Nihan S. Pol et al 2021 ApJL 911 L34. doi:10.3847/2041-8213/abf2c9

## Gravitational waves: Why the fuss? (Update)

A Laser Interferometer Gravitational Wave Observatory optics technician inspects the equipment that will be used to conduct tests in Pasadena, February 10, 2016

Q: What are gravitational waves?

A: Albert Einstein predicted gravitational waves in his general theory of relativity a century ago. Under this theory, space and time are interwoven into something called "spacetime"—adding a fourth dimension to our concept of the Universe, in addition to our 3D perception of it.

Einstein predicted that mass warps space-time through its gravitational force. A common analogy is to view space-time as a trampoline, and mass as a bowling ball placed on it. Objects on the trampoline's surface will "fall" towards the centre—representing gravity.

When objects with mass accelerate, such as when two black holes spiral towards each other, they send waves along the curved space-time around them at the speed of light, like ripples on a pond.

The more massive the object, the larger the wave and the easier for scientists to detect.

Gravitational waves do not interact with matter and travel through the Universe completely unimpeded.

The strongest waves are caused by the most cataclysmic processes in the Universe—black holes coalescing, massive stars exploding, or the very birth of the Universe some 13.8 billion years ago.

Albert Einstein (1879-1955), author of the theory of relativity, was awarded the Nobel Prize for Physics in 1921

Q: Why is the detection of gravitational waves important?

A: It ended the search for proof of a key prediction in Einstein's theory, which changed the way that humanity perceived key concepts like space and time.

Detectable gravitational waves open exciting new avenues in astronomy—allowing measurements of faraway stars, galaxies and black holes based on the waves they make.

Indirectly, it also adds to the evidence that black holes—never directly observed—do actually exist.

So-called primordial gravitational waves, the hardest kind to detect and not implicated in Thursday's announcement, would boost another leading theory of cosmology, that of "inflation" or exponential expansion of the infant Universe.

Primordial waves are theorised to still be resonating throughout the Universe today, though feebly.

If they are found, they would tell us about the energy scale at which inflation ocurred, shedding light on the Big Bang itself.

Q: Why are gravitational waves they so elusive?

Albert Einstein predicted gravitational waves in his general theory of relativity a century ago - they are ripples in space-time, the very fabric of the Universe

A: Einstein himself doubted gravitational waves would ever be detected given how small they are.

Ripples emitted by a pair of merging black holes, for example, would stretch a one-million-kilometre (621,000-mile) ruler on Earth by less than the size of an atom.

Waves coming from tens of millions of lightyears away would deform a four-kilometre light beam such as those used at the Advanced Laser Interferometer Gravitational Wave Observatory (LIGO) by about the width of a proton.

Q: How have we looked for them?

A: Before now, gravitational waves had only been detected indirectly.

In 1974, scientists found that the orbits of a pair of neutron stars in our galaxy, circling a common centre of mass, were getting smaller at a rate consistent with a loss of energy through gravitational waves.

That discovery earned the Nobel Physics Prize in 1993. Experts say the first direct detection of gravitational waves is likely to be bestowed the same honour.

After American physicist Joseph Weber built the first aluminium cylinder-based detectors in the 1960s, decades of effort followed using telescopes, satellites and laser beams.

Earth- and space-based telescopes have been trained on cosmic microwave background, a faint glow of light left over from the Big Bang, for evidence of it being curved and stretched by gravitational waves.

Using this method, American astrophysicists announced two years ago they had identified gravitational waves using a telescope called BICEP2, stationed at the South Pole. But they later had to admit they made an error.

Another technique involves detecting small changes in distances between objects.

Gravitational waves passing through an object distort its shape, stretching and squeezing it in the direction the wave is travelling, leaving a telltale, though miniscule, effect.

Detectors such as LIGO at the centre of Thursday's news, and its sister detector Virgo in Italy, are designed to pick up such distortions in laser light beams.

At LIGO, scientists split the light into two perpendicular beams that travel over several kilometres to be reflected by mirrors back to the point where they started.

Any difference in length upon their return would point to the influence of gravitational waves.

## Gravitational-Wave Astronomy

Einstein predicted that gravitational waves exist. What are they, how are they produced, and what is the evidence for their existence? We looked at ways in which colliding black holes and other violent events in the universe produce gravitational waves which eventually reach the Earth. Huge new detectors have been built on different continents to detect these signals. What they might tell us about the first moments of the universe, cosmic &aposstrings&apos and the highest energy events.

Professor John D Barrow FRS was Professor of Mathematical Sciences at the University of Cambridge since 1999, carrying out research in mathematical physics, with special interest in cosmology, gravitation, particle physics and associated applied mathematics.

Since its inception in 1999 John Barrow was the director of the Millennium Mathematics Project which aims to improve the understanding and appreciation of mathematics and its applications amongst young people and the general public. This has born fruit with the Project&aposs receiving the Queen&aposs Anniversary Prize for Educational Achievement in 2005. Further to this, he has received many awards and prizes for his own research in mathematics and astronomy, including the Locker Prize for Astronomy and the 2006 Templeton Prize.

He was the author of over 420 articles and 19 books, translated in 28 languages, exploring the wider historical, philosophical and cultural ramifications of developments in mathematics, physics and astronomy. He has also delivered lectures in a perhaps unique combination of locations including 10 Downing Street, Windsor Castle, the Vatican Palace and the Venice Film festival. He is also the author of the (Italian language) Infinities, which won the Italian Premi Ubu award for the best play in Italian theatre in 2002.

The appointment of Professor Barrow to the Geometry chair at Gresham College repeats a feat only previous achieved in 1652 by the founding member of the Royal Society, Lawrence Rooke. Having been a highly popular Professor of Astronomy between 2003 and 2007, Professor Barrow is only the second professor in Gresham College&aposs four-century history to have been appointed to two separate chairs.

Professor Barrow&aposs Geometry lectures complement the topics covered by his predecessors in the chair of Geometry Professor by focussing on the application of mathematics to familiar things. His aim is to show how mathematics is all around us and tells us many things about the world which we couldn&apost learn in any other way. The everyday mathematical problems that he will address reveal the importance of fascinating pieces of simple mathematics.

All of Professor Barrow&aposs previous lectures can be accessed here.

#### Transcript

Gravitational-Wave Astronomy
Professor John D Barrow FRS

Gravitational-wave astronomy

Professor John Barrow

One of the most striking ways in which astronomy advanced and became a more spectacular subject during the 20th Century was by extending the look that it gave us at the universe from just the optical band of light into other parts of the electromagnetic spectrum, so suddenly we had the capability to detect radio waves, infrared radiation, ultraviolet.  In this way, all sorts of different astronomies grew up – x-ray astronomy, infrared astronomy and so forth.  What I am going to talk about today is a further extension of astronomy that we believe is just beginning, which allows us to look at the universe in a new way, not in ordinary electromagnetic radiation, but through another form of radiation that is created by the force of gravity itself.  This is now known as gravitational wave astronomy.  We are going to see what gravitational waves are, how we believe that there is already evidence that they exist and we can see their effects, and some of the prospects for detecting them directly in the future.

Like many exotic features of Einstein’s General Theory of Relativity, there is a more straightforward Newtonian counterpart which it is best to understand first before you start grappling with Einstein’s conception on its own.  Gravitational waves have their counterpart in a familiar aspect of gravity.  Ordinary gravity has two manifestations that we are familiar with.  On the one hand, there is what I call direct gravity, so if you are a large mass and you put another mass up above it in space, the two masses will attract one another with a gravitational force which is inversely proportional to the square of their separation.

This is what I call direct gravity, and it is rather familiar, like Newton’s famous law of gravitation which we met at school, but there is another manifestation of the force of gravity that is different, although very familiar, and it is what we call tidal gravity or the effects of tidal forces.  Imagine that mass is just a point, that it has no finite size.  Whereas suppose we think of an object that has a finite size, so suppose it is a rod whose length is H, then the top of the rod will be attracted towards the mass with a slightly different gravitational pull to the bottom, because the top is further away, and so the top and the bottom are feeling different gravitational attractions, so you can imagine that there would be some stretching of the rod because there is a stronger gravitational force in some places than others.  This is known as the tidal gravitational force.  If you just use a little formula to work out the force on the bottom, at a distance R, and you use it again to work out the force when you are a distance R plus H away, subtract one from the other and you will have the tidal force, which is the difference in the force pulling the two points.  That force does not vary like an inverse square but as an inverse cube of the distance away.  This is the Newtonian tidal force, and it is very real.  We see evidence of it on Earth in a rather periodic fashion, and we refer to forces that have this differential character as tidal forces.  In the case of the Earth, the surface of the Earth is a rigid solid body, and two-thirds of its surface are covered by oceans, which are not rigid and are incompressible, and so the Moon exerts a gravitational pull on the Earth, the Earth’s body moves as a whole, there is not a significant differential which can move the Earth, but the oceans of course are shifted in a tidal fashion.  So the oceans are pulled toward the Moon, and what is happening is rather interesting.  The total volume of the ocean is conserved, and so if you pull it in one direction, you will necessarily have a push in the other direction. This is something that is characteristic of tidal forces: the overall volume, as it were, is conserved but the shape changes, so spheres are changed into ellipsoids, circles are changed into ovals.  So a large tide is rising, even though it looks as though there is no force acting on the point.

The Moon is not the only object that exerts tides on the Earth.  The Sun also has a tidal effect.  Very roughly speaking, the relative effects of tides on the Earth from things that you can see in the sky is proportional to their apparent size on the sky.  So Jupiter or Mars, which look absolutely tiny, have a completely negligible tidal effect on the Earth compared with the Moon.  But as you know, because we see complete eclipses of the Sun, the Moon and the Sun have almost the same apparent size on the sky.  It is one of the great coincidences of nature.  As a result, if we think of the Earth and the Sun, and possible positions of the Moon, the situation where you are going to get the biggest net tidal force on the Earth is going to be where you have an alignment between the Sun, the Moon and the Earth.  The Sun’s tides are about 42% of the Moon’s, so they are rather similar, although not exactly the same.  When things are aligned in this way, we say there is a spring tide.  Then you are getting a total effect which is about 1.42 times the tidal effect of the Moon alone, and that is no doubt when you want to put up the Thames Barrier and things like that.  At 90 degrees, when the Moon is in one of these positions, then we have what is called a neap tide - neap is just an old English word meaning weak or feeble – and in those situations, the tidal effect is a minimum and it will be about 56% of the effect of the Moon alone.

These are simple manifestations of tidal forces.  What is curious about these tidal forces is that they are what mathematicians call transverse.  This is like the effect of changing the sphere into the ellipsoids, the Earth’s tides, so they produce accelerations and effects perpendicular to the direction in which they are acting.  Remember, the direct gravity pulls the two points together along their line of centres, but the tidal force produces that distortion at right angles to it.  So that is the idea of a transverse acceleration or a transverse force.

Now, in general relativity, we see exactly the same phenomena acting in rather more exotic ways. Einstein teaches us that we should think of space as not being an untouched cosmic stage on which all the heavenly bodies’ motions are played out, but something which is affected by the motion of matter and energy upon it and which in turn can affect the way in which matter and motion take place.  So instead of thinking as if it is a stage, we think of it rather like a rubber sheet, a trampoline as a large mass moves around on it, it deforms the shape of the trampoline, and the larger the mass, the greater the deformation.

If I was to introduce another object and to fire it from A to B, if it moved in such a way so as to minimise the time that it took to get from the first point to the second, then because the geometry is distorted by this mass, the shortest path is to take a slightly bent route that makes it look as though you are being attracted towards the central mass.  So if you were a Newton, you would say there is a force acting which is attracting you towards that large mass, but Einstein’s picture is not to talk about forces at all, but just to have a view that this mass distorts the geometry and everything moves so as to take the shortest path that it can on whatever geometry it discovers.  And so if you want to take a path, then you have to take a very bent path, and Newton would say you were feeling a very large force.

Once you have taken up this picture of the curved space, distortion of space and distortion of time as well, created by mass and energy, you have two other things that could happen.  On the one hand, if you spun an object, if you twisted it around, then in the Newtonian picture, nothing would happen.  So if we spin a top in one place, it does not affect somebody standing elsewhere.  But if you had the picture of a rubber sheet distortion of space time, then if you twist the rubber sheet in one place, it makes it move around and fire away, you get carried around in the same direction.  So spinning objects have an effect on things which are far away.  This is not an effect that you would see in Newton’s picture of the world.  There is a satellite project at the moment which is flying gyroscopes around the world to watch how their direction of rotation, of the gyroscope, gets dragged around in the same direction that the Earth is rotating. It is a tiny effect, but it should be unambiguously observable.

But today we are more interested in the second effect of having this rubber sheet picture.  Suppose I grab hold of the edge of the sheet and start waving it around, producing waves, ripples in the geometry, then these will spread across the sheet.  They will behave like waves.  If you are sitting at one place when one of these ripples passes you, you will move up and down and in other ways you will respond to this movement of the curvature passing through space.  As they get further and further away, they should get smaller and smaller and smaller, and gradually damp out.  So if you are a long way away from the source of these ripples, violent events perhaps, you will see much bigger effects than if you are far, far away.  This effect of the rippling through space time, is the relativistic Einstein version of the tidal forces of Newton that we have just been looking at, and so we expect that it is going to have the same type of effect.  These ripples move at the speed of light and they also have an effect just like tidal forces.  So if there is a ring of particles, in front of me, and one of these gravitational waves comes in from the ceiling and goes downwards, it expands the ring in one direction and compresses it in the other direction, so it turns the circle of particles into an ellipse –just like the tidal force.  This is the reason why we think of this rather like a Newtonian tidal force.  More graphically, this is the effect on you.  There are two sorts of effect: you could find yourself being stretched in one direction and being squeezed in one direction or, just like the hall of mirrors on the pier at the seaside, you could find yourself being squeezed in one direction and stretched in one direction.  This is the effect of a gravitational wave which is coming through the projector from above, or coming up from below.

More technically, it is interesting to look at that effect in comparison with other sorts of waves that we meet in physics, like those of electromagnetism.  Electromagnetic waves, when they pass through a ring of particles, cause every particle just to move backwards and forwards in the same way.  So when light hits your eye, it causes a movement, which creates little electric and magnetic fields, which then send a signal to your brain.  They hit a photographic plate those movements call little chemical signals to record light having fallen on the emulsion.  In the case of gravitational waves, each particle behaves differently, and we have an effect where some of them move out and some of them move in.  So gravitational waves are not like ordinary electromagnetic waves.

If we look at the same idea again, reinforce this idea, there are two types of action, two modes of distortion that a gravitational wave would produce.  You start with a ring of particles, and as the wave comes in, as time goes on, you first create an ellipse of particles, and then it oscillates back to the circle, back to an ellipse of the other orientation, and then back to where it started.  This other sort produces an inclined ellipse, back to a circle, back to an inclined ellipse, back to where you began.  So as time goes on, this is the signal that you would expect to see in your particles that you might be suspending in space.  You can watch them expand and contract in one direction and then in the other.  So the challenge is to exploit this feature in some way in building a detector to try and tell when this sort of wave energy has passed through it.

One way that you might set about trying to gauge this is to say, well, let’s measure the magnitude of the effect by looking at the little change in distance, so let us look at the change that happens to the particles that move up there, the little shift in their position, divided by the radius of the circle of particles. This would be the relative shift produced by the gravitational wave.  Here, things get a bit alarming.  So you define a famous parameter in this subject which, for reasons of history, it is just twice the shift – it is the shift across the diameter divided by the radius of the circle of particles – and you know a few things about this quantity, that if you try to throw in a gravitational wave that was too strong, fantastically strong, you would bring in particles in one direction so dramatically that you would create a black hole.  So there is a sort of ultimate no-go for this type of phenomenon, that if you have the parameter “H” trying to be bigger than this quantity, where this is the mass of the object that you are hitting, “R” is its radius and 𠇌” is the speed of light, then it would be torn apart by the gravitational waves that are coming through.

Let us look at a simple example that is realistic.  Suppose we had a neutron star, 1.4 times the mass of the Sun – that is the smallest it could be – and we put it 50 million light years away, then if we put 50 million light years in, put the mass in, and “G” and 𠇌”, and work out the number, it is 6 times 10 to the minus 21.  So this is fantastic, fantastically small.

To give you an idea, suppose you were looking for a relative shift in a detector that was a couple of meters long, so the radius of the circle would be a meter or so, then you are looking at a shift that is about 10 to the minus 21 of a meter, 10 to the minus 19 of a centimetre.  That is one millionth of the size of a single proton.

So your first guesstimate is that the effects of these waves are fantastically small, so you have got to either have some stupendously accurate type of detector, or you have got to look at something that is closer and much more violent than a simple neutron star.

When one looks more carefully at what this source of this perturbation might be, you realise that you can do rather better than this formula, that what is creating the gravitational waves is not all of the energy involved, it is just the energy that is producing non-spherical pulsing and oscillations, that is changing the shape in that non-spherical way.  So it is even harder to do, if you had a very strong gravitational field created by a perfectly spherical object, and the spherical object was just changing its radius, but not its shape, going backwards and forwards like a balloon being inflated and then deflated, but always perfectly spherical.  There would be no gravitational radiation at all.  So the gravitational radiation is produced by the asymmetrical, non-spherical movements of an object.  You can regard “H” as being a bit like the “G” and the speed of light squared, the distance away times the energy, the kinetic energy, in the elliptical and non-spherical motions, divided by the speed of light squared.  It is these speeds of light squared that sit in at the bottom here which are very large numbers – so C squared is 10 to the 21 centimetres squared per square second.  This is why this effect is so small.

Let us first look at the sorts of places where you could go searching for effects of this sort, and then think about how you might detect them.  There is a little list of prime candidates.  Anywhere in the universe where you see something rather violent and dramatic going on is likely to be a good source of gravitational radiation.  Exploding stars, like supernovae, are good candidates.

A few years ago, I think it was back in 1987, there was a supernova in the nearby dwarf galaxy to ourselves called the Large Magellanic Cloud.  An astronomer in Australia was looking at a plate in real time, they had just taken a photograph of a bit of the sky he looked again a few minutes later, and suddenly the whole of the image was burnt out on the plate.  A star had exploded in that other galaxy, which he had caught virtually in real time.  In fact, after that explosion, people realised that had gravitational wave detectors been turned on in places where they existed, they might well have seen some gravitational wave signal from this explosion.

So supernovae are one candidate.  It turns out another candidate, really the best of all, is a situation where you have a pair of neutron stars or a pair of black holes, which orbit around one another, rather like the Earth and the Moon do, but after a long, long period of history of doing that, they gradually run out of energy, they get closer and closer to one another, and eventually they merge.  That merger event, which could be quite a common occurrence because there are so many of these pairs around in our galaxy and beyond, gives the most ‘seeable’ burst of gravitational radiation.

Another possibility is something that is periodic, like a pulsar.  It is just orbiting around another object, in a very asymmetrical orbit, and would give a signal of gravitational waves that had a periodic pattern representing its orbit.  That is another possibility.

The others, that astronomers are very interested in, are gravitational waves which are just produced by all sorts of things, all over the place, some exotic, some not so exotic, perhaps the early formation of the first galaxies, and all these would just get added together, rather like background noise in a radio signal.  You might hope that one day you could discover this random background of gravitational waves being added together from all the sources in the past.

The last one, which I will not say anything about today because my next lecture will say quite a bit about this in another context, is that we expect that there should be very particular types of gravitational wave left over from the beginnings of the universe, and it is a great challenge to try and detect them and to check whether they have the particular properties that are predicted, the particular pattern of energies.

We will now have a look at one of the most interesting situations.  It is one of these binary stars, and it is one we have met before in another context in these lectures, and it is the so-called binary pulsar.  This was discovered in the early 1970s by Hulse and Taylor and they received the Nobel Prize for this discovery some years later.  What they discovered were two objects orbiting around a common centre.  These objects seemed to be neutron stars, so they had a density equal to a single atomic nucleus, 10 to the 14 times the density of ordinary material around us now, and yet their size is just about 3 kilometres.  So they are incredibly dense.  If they were just twice as heavy as they are, they would be black holes.  These are both of mass of about 1.4 or so solar masses and one of them has the remarkable feature that it is a pulsar, so no doubt it is spinning fantastically rapidly and, rather like a lighthouse, when it spins and faces in our direction, we see a pulse, and we see a pulse then in a period of time equal to the spin time.  So this pulsar is like a clock.  It is an object moving around with its own clock attached, and the pulsing period responds to the gravitational field that it is in and enables us to make fabulously accurate observations of what is going on in this system.

These objects in this system, so dense are they and so close together, that these orbiting stars are moving at one per cent of the speed of light, so they are objects a little more massive than the Sun, about the size of a small part of London, moving around at one per cent of the speed of light.  That is about two miles per second or something like that.  What you can focus on in this system, as they go around, one is going around the common centre, to a first approximation it is orbiting in an ellipse, but the ellipse never quite closes up, and if you follow it from one orbit to another, the ellipse is slightly displaced, by a little more than 4 degrees each time it goes around many, many orbits.  You could measure what is going on by, for example, working out what this angle is, how much the orbits get displaced, and the displacement amounts to about 4-and-a-third degrees every year.  In the case of our solar system, you see an analogous phenomenon for the planet Mercury.  It advances by 43 seconds of arc every century, so this is fantastically bigger.  This system has very, very strong gravitational fields.  It has non-circular motions.  It is a prime site for searching for the effects of gravitational radiation.

Here are some of the statistics about it.  The nice thing is that each one of these orbits takes less than 8 hours to complete, so you can watch, in real time, what is going on in this system and observe it in enormous detail.  The pulsar period is very slowly changing, and the rate at which it is changing are a few parts in 10 to the 12 seconds per second, so if the orbital period is in seconds, you are interested in how much did it change per second.  This is an incredibly small number.  It is a reflection of how accurately you can measure the period of the orbit of this system.

But why is this interesting and what has it got to do with gravitational waves?  Well, if you use the formula that tells you how much of the energy is involved in produces distortions in the shape as it orbits around.  In this system, as the 2 objects move around their common centre, they should gradually lose a small amount of their energy by gravitational radiation going away from the system.  As they lose energy, their orbit gets a little bit smaller, and they will get closer together.  What you expect is, as time goes on, the system will lose energy by gravitational radiation, the objects will get closer together, so the period of their orbit will get smaller.  We can predict, from the formula for the amount of the rate of gravitational wave production, exactly how much we expect the orbit to shrink by as time goes by.  You can use this prediction then as a test of whether gravitational radiation is really leaving this system, and leaving it at exactly the rate that general relativity predicts.  Over 25 to 30 years, the results of this experiment are very remarkable.

When you reach a particular point on the orbit, so it is giving you a measure of the shrinkage of the orbit, and time, in years, from the discovery – 1974 – up to the present year, or last year.  This is the prediction from general relativity of how the orbit should decay if it is losing energy by radiating gravitational waves, and there is a beautiful agreement to this 12 decimal place accuracy in effect of how the orbital period should change.  Most astronomers would regard this as a very, very powerful indirect discovery, that gravitational radiation does exist and it is being radiated by this system at exactly the rate that Einstein’s theory predicts that it should be.

The challenge resulting from this is to try and find ways to detect radiation like this directly, so when it reaches the Earth, can you see its effects directly?  Well, the prime candidates are systems a bit like the binary pulsar.  Its motion is causing ripples in the geometry of space time around it.  Those ripples are moving away.  They eventually reach us.  But when the orbit decays enough, it will start to speed up dramatically, and eventually the objects will coalesce and collide.  So we are looking for objects which are like the binary pulsar, but in the final stages of their lifetime, when they have produced an incredibly strong nearby gravitational field and they are both about to go bang.  That is the most ‘seeable’ event, and we see lots of binary pulsars around in different stages of maturity.  So it is not that the binary pulsar was a very special, unique event that we do not have any reason to find anywhere else.  They seem quite common phenomena.  Most stars are in binary pair systems, and there will be other ones which are heavier still, where the two objects are not neutron stars but they are black holes, and they will produce even more gravitational radiation.  So in many ways, these are the most interesting prime candidates for gravitational waves.

Astronomers produce simulations, by computer, of what would happen in detail when one of these coalescences occurs. They can produce a picture, colour coded by radiation intensity, being squeezing out in one direction, coming in in another direction, as these 2 objects coalesce.  The reason for doing this is that you want to predict in enormous detail what should be the profile, what should be the pattern, of the gravitational wave energy that comes out of one of these objects.  So if you detect something in your experimental detector, can you identify it, can you say “oh, that’s a binary star system that’s coalescing,” or is it a supernova, or is it something else?  Can you really do astronomy one day with gravitational waves?

I have 3 pretty pictures, just to remind you of these scenarios.  The colliding, orbiting neutron stars, eventually their collision to form gravitational waves in the merger event.  They might eventually themselves settle down to form a black hole, or the formation of a black hole might be a completely different violent gravitational event.

The most interesting thing of all to try to predict and understand is the magnitude of the signals that we should get from events like this.  So that parameter “H” that we mentioned before, so if you had a ring of particles, as it were, and a gravitational wave is going to hit it, it stretches and squeezes, this is the amount of stretching divided by the size of the detector.  There are very, very small numbers – 10 to the minus 18 to 10 minus 24 – and the frequency of the radiation.  This will depend on the size of the source and how quickly it is varying, and you want to build your detectors so that they are most sensitive in places where you expect there to be most signals or the most visible signals. You have what are called compact binaries: these are very close pairs of stars, rather like the binary pulsar.  You have got an example of 2 black holes in a binary system.  They could be much, much bigger, 100,000 solar masses each.

There is a model for an event for forming a black hole of about that size - 100,000 solar masses – so the burst of radiation you get from that.  Then there is what happens if that black hole binary pair eventually spiral in and coalesce and merge, and that is really the biggest of all.  You have got supernova formation, exploding stars, and so on.  We are dealing with numbers of order 10 minus 20.  In the case of the smallest things, we are identifying smaller black holes, going down to about 10 minus 23.  Supernova collapse, depending on how close it is, how asymmetrical and non-spherical it is, you have got a wide range of possibilities, and the frequency range spans a factor of about 10 to the 7, 10 to the 8.

The other curves are marked LIGO and LISA.  What they are showing us are the expected sensitivities of the detectors. Obviously those detectors were designed and planned with the express intention of covering these crucial areas where we expect the signals to lie.

What are the detectors like?  When the subject first began, long, long ago, the �s and the �s, the original detectors that people had in mind were enormous metal bars that would weigh many, many tons: a great cylinder of metal, perhaps a metre in diameter and several metres long.  What you wanted to do was to try to detect what happens when a gravitational wave passes through your bar - it will stretch in one direction and contract in the other - and you try and tune the mechanical properties of the bar so that you get a resonance between the natural vibration frequencies of your bar and those of the gravitational wave.  As always in this subject, the trick is not being able to detect these tiny effects, but making sure you do not detect anything else.  So you have to suspend the bar in as good a vacuum as you can possibly make, at low temperature you have to isolate it from all seismic disturbances, like football teams running past next door or people driving cars around, or even physicists walking around next to it.  This is a fantastically challenging problem.  Bars were the first generation of detectors.  There are still some gravitational wave bar detectors that exist.  They have a sensitivity, at best, 10 minus 18, so they are severely limited by their internal mechanics and the extent to which you can remove noise.

One of the other things that you wanted to do in that type of detecting work, if you had one bar and it suddenly deflected in some way and you claimed to see a signal, people might not believe you.  They might say it is the football team running past.  So what Joe Weber, who was one of the pioneers of this, wanted to do was to have 2 of these detectors in very different places.  In his case, it was in different states in the United States – Illinois and in Maryland – and you would monitor the signals in each one, and of course, if you found a signal in one which you did not see in the other, it is probably the football team, but if you see the same signal in detectors on other sides of the country, it is very likely to be a real signal.

The problem historically was that when Weber first set out to do this, he claimed after a while that he did see signals for a long period.  Nobody else believed him at the time, and I think even now, no one believes that he really saw gravitational waves – he could not possibly have done at that time, unless there was some sudden outburst that just happened then and disappeared ever after.  Weber died some years ago, so we cannot ask him any more what he was really doing, but Weber was a great pioneer in the building of detectors.

But if you want to really see gravitational waves, enormous bars are not the way to go, so there is another technology which enables you to get down to these fantastically small numbers, and what that technology is is interferometry.  What you want to do here is you imagine that we have got a crossover, gravitational waves coming in from above, and so what it is going to do is it is going to stretch things in this direction, and it is going to squeeze them in the direction at right angles to them.  How can we exploit this in a detector?  Well, interferometry has the following type of set-up.  Suppose you have a laser beam, and you fire it into a beam splitter, so this is something that allows, say, half of the light to go on through, but reflects half of it at right angles.  Half of the light goes on through and eventually meets a mirror at the end, a suspended mirror, and so is reflected back the light that has gone at right angles has the same fate, gets reflected back from a mirror, and so the 2 beams meet again at the centre.

This is the secret of fabulously accurate measurement in physics, so that you can measure a mismatch between the oscillations of those light beams when they come back together in the middle to fantastic accuracy.  You can keep on making the accuracy almost as good as you like by simply making these arms longer and longer, so the longer you make the arms, the more time there is for the light to feel the effects of the gravitational wave, as it goes out, hits the mirror and comes back.  If you want to make the effect twice as big, you make the arm twice as long.  If you want to make it a thousand times more sensitive, you make the arms a thousand times as big.

This is the essence of laser interferometry, and there are all sorts of cunning tricks that you can now employ to make the sensitivity ever greater.  The laser beams are all confined inside a low temperature environment, so that everything is kept as cold as possible, so that jittering due to thermal agitation is absolutely minimised.

The next thing you are interested in is generating lots of laser power, and that is a technological challenge.  When you send your beam back, you need not just send it once before you check whether the interference occurs with the orthogonal beam you could put silvered mirrors and send the beam back and forth millions and millions of times.  This would have the same effect as making the arm fantastically longer, but as a constraint, the silvering of the mirrors had better be extraordinarily good, otherwise you get a degradation of the signal.  This is one of the great technical advances of this gravitational wave experimental development - I think it probably counts as one of the highest technology areas of science - so this type of astronomy has pioneered the most accurate detectors anywhere in science anywhere on Earth.

I can remember being involved in the European appraisal panel that had to decide whether to fund the big European project of this sort many years ago, and there was a remarkable development during the appraisal process that there had been people around the world who had tried to estimate how good you could make a detector like this, and that they had produced an argument that there was a fundamental limit to how good you could produce a silvered mirror to reflect the laser beam back, and this placed a limit on how well you could do the experiment.  Then, rather unannounced and completely unexpectedly, British Aerospace declassified some of their work on high silvering coatings, so presumably this was all something to do with Star Wars and bouncing laser beams around, but it turned out that they had fully functioning, working mirrors, which had reflectivities 10,000 times better than the so-called absolute maximum possible!  So overnight, they made some of these super-high-tech surfaces available for this sort of experiment, and you had a massive increase in expected capability.

These are the key ingredients.  You have also got to suspend these mirrors.  They are very heavy masses – they are the things that the gravitational waves when they come through are shifting and wobbling in different directions, and you are trying to detect that tiny wobble by its effect on the reflected laser beams.  By making the arms extremely long, you can get the sensitivity that you require.  By long, I really mean long.  The existing project, which is known as LIGO, so the Laser Interferometer Gravitational-Wave Observatory – one of the political things you soon learned about this area of the subject, that suddenly gravitational wave detectors started to be called gravitational wave observatories, so that means they can make bids for astronomical funding rather than just for physics funding!  So if you call it an observatory, it is astronomy, and if you call it detector, it is physics!

For example, in the USA, there are 2 stations like this, so again, you want to have more than one so you can play this game of saying, “If we see a signal and you see a signal on the other continent, it’s likely to be a real signal, but if we see a signal in only detector, people won’t believe you.”  So in these 2 places, in Louisiana and in Washington state at Hanford, there are huge L-shaped interferometers, and by huge, I mean these arms are 2, 3, 4 kilometres in size, and they are also bouncing light back over a long period of time.  The timer period is determined by how good your reflectivity is.  So you have surfaces with a reflectivity good to a part in a million, and so that enables you to use many more bounces of the light, effectively increasing the length of your arm.

I have a couple of photographs of those American stations, to give you the idea of the scale.  Of course, it’s in the middle of nowhere so that you are not bothered by the football team.  So where there is one arm, there will be another one perpendicular to it, and another one going through the desert.

There is also, as I mentioned, a European, in fact a UK, presence in this project.  The UK, through the group at Glasgow, has played a key role in developing the technology that can actually make this detection.  The European group does not have a site which enables you to fit 3 kilometre arms in undisturbed in some desert, so the European project is based in Germany, in Lower Saxony, and it has a 600 metre arm, and it is known as GEO600.  That is very much used for developing the next stage of the technology – better suspensions for the mirrors, better silverings, better laser technology, and so forth.  The key is to have 2 detectors, on opposite sides of the American continent, one in Europe as well, and in the future, there will be operating detectors in the Far East and the Southern hemisphere as well.

Has anything been seen by these detectors?  Well, for many years, it was constantly a game of improving your sensitivity, making sure the lasers as stable over long periods of time but, a couple of years ago, the first engineering runs started to be operating in this experiment.  This was very exciting.

No one is claiming to have detected gravitational waves yet.  What they are trying to show is how sensitive the detectors are.  There have been relentless and impressive progress. The sensitivity is down around 10 minus 21, approaching 10 minus 22. One can see things in 10 minus 21, 10 minus 22, if you are lucky.  You could see something, if you took to pieces all the signals, analysed them in detail, you would be capable of seeing some of these events, but people are really expecting that the most probable events are going to be really down near 10 minus 22 and below.

There is no doubt noise.  It is different sources of randomness and noise in the detector, fluctuations in the lasers.  You have a procedure for cleaning this and removing all those things, and you want to then look at what’s left.  The next stage in the game will be, when you have improved your sensitivity a bit more, to start doing that cleaning much more seriously, and to start arguing whether or not there are residual signals.

What would you do with them?  How do you go about saying whether signals are real or if they are just some form of noise?  There are many research groups around the world who spend their time calculating in enormous detail what you would see if your detector was hit by a real gravitational wave signal.  Unfortunately, in many cases, the pattern of the signal is relatively straightforward – the real signal – and you can predict in enormous detail what you would see as time went on, and produce a series of templates.  This is the magnitude of the fluctuations in “H” against time, and it is the binary pulsar in effect, so what would happen the binary pulsar when it came to the end of its life – 2 neutron stars spiralling in until they eventually hit one another.  The frequency of the radiation is going up, so it is like a chirp, birdsong, change of frequency, in this case going up, rather steadily going up, and then finally, when the merger occurs, there is a rather sudden burst.  This would be what you would call a template.  You could make a template of this sort for all sorts of different types of merger, adding all sorts of complications, which are not present here, and a computer will overlay your data stream with these templates, and it is looking for a match, looking for a suspicious situation.  It is rather like a fingerprint analysis: you are looking for the fingerprint, some matching features, of the gravitational wave burst in time, and then you focus in on that part of the signal in enormous detail.

So that is the state of play with LIGO, and we all hope that over the next few years there might begin to emerge some evidence for a real signal.  It is rather amusing that when this began, I think in 2004, that Ladbrokes were offering odds of 500 to 1 against a gravitational wave being detected by LIGO before 2012.  So all the people involved in this experiment immediately went out and took those odds, and apparently, 4 weeks later, the odds were down to 2 to 1!  This is very gratifying, that the odds are now actually only 2 to 1 that we will detect a gravitational wave by 2012.

But the last thing I want to show you is something yet more ambitious, regarding where we might hope to get to with a detector. LIGO is looking for the coalescences.  There is another detector range, which is called LISA.  LISA is a laser interferometer, as before not on the Earth’s surface, but in space.  This is a planned project in which one will have orbiting in the solar system a trio of satellites, and they will send laser beams to one another and around the triangle, using their highly reflective surfaces, and of course, being in space, we don’t have problems of temperature fluctuations or football teams running nearby.  You have some analogous problems.  The interesting thing is that instead of having the arms of your interferometer a few kilometres in size, you can have them as half the radius of the solar system.  This space project will be monitoring laser beams moving around this triangle, looking to see if you get little interference patterns created by a gravitational wave that comes through the centre of the triangle, as it were, causing some arms to expand in this direction and these to contract.  This is a spectacular future space project that is more than on the drawing board, it is planned in enormous detail, and the hope is that in combination with LIGO on the ground, we will by this means finally detect gravitational waves directly.

As we will see in my next lecture, in a couple of weeks’ time, that will not only confirm that these objects like black holes and neutron stars really are shaking the structure of space and time, they will allow us to look back to the first instance after the beginning of the expansion of the universe commenced, far, far further back than the background radiation of photons allows us to see.  Gravitational waves allow you, as it were, to surf the universe in a new way, and in years to come, we expect that this will be a new type of astronomy.  It is the astronomy that doesn’t just look at visible light or other parts of the electromagnetic spectrum, but you can view it as looking at tidal gravitational forces directly.  It is a probe of the places where the most violent things are happening in the universe, and look at the force of gravity very directly.

## GRAVITATIONAL WAVES: AN INTRODUCTION TO RIPPLES OF SPACE-TIME

The article explores and explains the evolving concept of “gravitational waves”. It presents the importance of and recent progress in the contemporary knowledge of “gravitational waves”. It provides a brief overview of the interferometer – an instrument used to measure these gravitational waves. The article elucidates how the detection of “gravitational waves” has helped astronomers, physicists, and scientists to amass conclusive scientific evidence to provide evidence for theories like the “Big Bang” and Einstein’s “Theory of Relativity”. A reference to the works of LIGO and Virgo observatories and their findings have been discussed to explain the impact of “gravitational waves.”

Astrophysics Gravitational Waves Gravity Waves Accelerated Masses LIGO and Virgo Observatories Blackhole Neutron star.

Introduction

The landmark invention of the modern telescope in 1609 by astronomer Galileo Galilei marked a milestone in human advancement for detecting light from distant bodies in space. It opened new doors to discover and understand the nature and behavior of celestial bodies and many complex and unknown phenomena in space, which was not possible earlier due to limitations of resources and technology. For a considerable amount of time, making observations primarily using one’s vision (with or without a telescope) was the only way astronomers could provide strong evidence about how the Universe works. Humans are bound by the limitation to only observe substances interacting with light. This barrier was proved to be evident when it was discovered by scientists that light travels enormous distances in the universe and reaches Earth as waves with longer wavelengths that were invisible and could not be observed by optical methods. When light covers huge distances in space, its wavelength gets stretched which in turn converts it into longer wavelength electromagnetic radiation such as infrared. These cannot be detected by optical telescopes. Therefore, there was a compelling need to develop technology to enable the detection and study of such other waves in the electromagnetic spectrum. The evolution of telescopes from detection in the visible spectrum to invisible spectrum has helped astronomers avoid cosmic barriers and accurately study many phenomena. For instance, the Spitzer telescope was a major invention that detected infrared radiation from celestial bodies at enormous distances. This was one of many telescopes that brought technology and astronomy together. The Fermi Gamma-ray Space Telescope was launched in 2008 to study energetic phenomena taking place in the universe such as gamma-ray bursts, pulsars, and diffuse gamma-ray emission. However, yet another limitation astronomers face is that there remain many barriers to detect radiation in the Electromagnetic Spectrum, which dilutes the image of the universe. Electromagnetic radiation (ER) interacts with matter and hence can be absorbed, reflected, refracted, or bent. This reduces the prospect of gathering concrete evidence for a theory to be accurately proven [1]. Besides that, it prevents astronomers from discovering and detecting celestial bodies and other relevant phenomena in the universe. The challenge was accepted by the astronomers and scientists whose relentless and diligent efforts in the race to attain absolute assertiveness in predictions, invented and devised new mechanisms and phenomena. Research of “Gravitational waves” (GW) turned out to be quite promising.

Gravitational waves, also recognized as gravity waves, are disturbances in the fabric of Space-time [2]. The existence of gravitational waves was first predicted by Albert Einstein in 1916 in his “General Theory of Relativity” [2]. Einstein theorized that when enormous masses are in acceleration (like a system of binary neutron stars [3]), this would disrupt space-time in such a way that waves of undulating space-time propagate in all directions away from the source [2]. This may be visualized as ripples or waves on the surface of water, though one cannot observe gravitational waves. Hence they are also referred to as “ripples” of the surface of Space-time. Gravitational waves interact very weakly with matter in space, which helps astronomers design a fairly clear image of the universe. The waves carry cosmic information that is free of distortions (unlike ER, owing to its tendency to interact with matter). The Laser Interferometer Gravitational-wave Observatory (LIGO) located in The U.S. and the Virgo interferometer located in Italy are currently the only two interferometers used to detect gravitational waves in space-time. These observatories have been working together, focusing on the detection of gravitational waves in space-time to observe and understand various cosmic phenomena. When GWs are produced by rotating pairs of neutron stars or black holes, they are detected by the LIGO and Virgo observatories.

Importance and future scopes of Gravitational-wave research:

The current focus of the LIGO and Virgo collaboration is on binary black holes and neutron stars. These are such powerful events that the gravitational waves that release thousands, millions, or billions of light-years from our planet, can still be detected from Earth. These GWs help us understand such energetic phenomena, and provide solid proof of Einstein’s Theory of Relativity. Gravitational-wave detection is now on the path of satisfactorily providing evidence of some of the earliest and unimaginable cosmic phenomena like the “Big Bang”. The technology for gravitational wave detection has started to evolve and currently, there are plans of building an observatory in space called “LISA” (Laser Interferometer Space Antenna), which would provide very accurate results, furthering our understanding of the universe.

“Gravity”: Do we know enough about it?

A common person is aware of this “attractive force” called gravity, but it goes much deeper than that. The basic definition of gravity according to physics, is that an attractive force is exerted by everything which has a certain mass that influences its surroundings. However, things get more peculiar when we start to learn about modern physics which includes the study of Einstein’s famous “Theory of Relativity”. Space-time is a fabric – as suggested by Albert Einstein – where an object with mass will exert the force of gravity in such a way that the space curves around the object. One can visualize this with a very simple experiment. Take a ball and place it on a stretched bed-sheet or cloth. The observation is, it creates a depression in the bed-sheet due to its weight. Similarly, due to an object’s mass, it exerts gravity of its own and hence creates a depression on the surface of space-time fabric. The idea has been pictorially depicted in Figures 1 & 2 below, for better comprehension.

But when one considers large masses like neutron stars the influence of gravity on Space-time increases and it increases even more if the star is rotating or is in an orbit with another star recognized scientifically as Binary Star Systems. They are extremely dense and highly accelerated and due to this energetic phenomena, distortion of space-time occurs forming “Ripples” on the surface of space-time fabric which are released in all directions outwards from the source. One can visualize this phenomenon by taking a tumbler of water and then putting a hand blender in it. The observation in this case will be pretty simple to conclude when the blender is switched on, its blades spin and produce acceleration, due to which ripples or waves can be seen on the surface of the water. This is similar to the above astronomical phenomena of the formation of gravitational waves on the space-time fabric. The only complexity remaining is that they can only be detected, not seen. An attempt to pictorially explain the cosmic phenomenon is done below in Figures 3 & 4.

For a deeper understanding of the concept of gravitational waves, it is mandatory to understand the answers to the following inquiries:

1. What causes gravitational waves?
2. What can be the impact of gravitational waves on earth? Does every detected gravitational wave have a potential adverse impact on earth? What kind of accelerated masses are helping scientists detect Gravitational waves?
3. What are the instruments currently used to detect the gravitational waves? How do they work?
4. Is there any theory based on gravitational wave evidence to prove or at least claim our evolution?

What causes gravitational waves?

Gravitational waves can be caused by many cosmic phenomena, but to date, the detections revealing the sources of gravitational waves are limited to rotating and colliding neutron stars, black holes, and supernova explosions. There can be many other cosmic phenomena causing distortions in space-time. However, due to the current limitations, the discoveries of the existing sources are considered the best possible way to analyze and understand gravitational waves. The detected waves are not of massive magnitude to cause distortions to earth due to the loss of energy of these waves over enormous distances in space.

What can be the impact of gravitational waves on earth? Does every detected wave have a potential adverse impact on earth? What kind of accelerated masses are helping scientists detect gravitational waves?

One can say a “distortion effect” from gravitational waves causes the earth to expand at one part and compresses at another (provided, it reaches Earth, after traveling an enormous distance in Space). However, scientists have not recorded any significant impact so far on earth, caused by such a cosmic phenomenon. This is because they occur many light years away from earth so the Gravitational waves from that particular phenomena lose a significant amount of their initial energy. Therefore, we hardly observe or record any distortions. This would only be possible if the earth was sufficiently close to the site of phenomena. Instead what the earth receives is so small in magnitude, that scientists can hardly detect it without proper instruments like the laser interferometer.

Back in 2015, scientists in the LIGO and Virgo collaborations were successful in detecting these waves released 1.3 billion years ago due to the collision of two orbiting massive black holes. This provided supporting evidence for Einstein’s Theory of Relativity. Other than this LIGO has detected 50 distortions which include other massive stellar objects like rotating asymmetric neutron stars.

What are the instruments currently used to detect the gravitational waves? How do they work?

The Interferometer was developed by a scientist Albert Michelson in the 19th century. The instrument is used in many different research experiments to measure minute changes in experiments. As the name suggests, it works on the principle of producing interference patterns from two or more sources of light by reflecting them on mirrors placed at certain specified distances and angles [4]. With the invention of the “laser” (Light Amplification by Stimulated Emission of Radiation), the basic model of Michelson’s interferometer has evolved. The latest invention being the laser Interferometer, and also the largest being deployed in the US by “Laser Interferometer Gravitational-Wave Observatory” or LIGO for short. It works on the principle of generating interference patterns from a single source of laser light.

How does the Interferometer work?

The laser light from the single source travels down two arms of the vacuum chamber (which are placed perpendicular to each other) by the reflection of a mirror which splits the laser into two separate beams. The mirror splitting the beam into two is placed at a 45° angle from the source of the laser. The vacuum chamber helps to avoid the interaction of lasers with particles of matter or gas in order to prevent distortions to the beam.

The laser light hits the surface of two mirrors [5], (each placed at the very end of the two arms respectively) and gets reflected. The laser beams retrace their path back from the two consecutive arms down through which they were initially propagated.

The two laser beams reach the first mirror placed in front of the source. The laser beams recombine back at the base. The Rays lineup in such a way that they cancel each other out. The peaks and valleys of the two light waves align oppositely (i.e. the valley is aligned just above the peak) so that when they both are added together we get a zero or they have a nullifying effect.

When a gravitational wave hits the interferometer it distorts space-time Consequently, the mirrors move from their original position (for about 1/10 th of the diameter of a proton). This interferes with the two laser beams, disturbing their original alignment, and thus, they no longer cancel each other out. As a result, in the newly disturbed condition (parallax error), the laser beam falls on a detector. This is proof of a gravitational wave being detected. A series of continued distortions, which each time needs to be measured with maximum precision provide evidence that the signals are gravitational waves. A diagrammatic representation of the types of interferometers can be seen in Figures 5 & 6.

So far, LIGO has made a number of confirmed detections of gravitational waves and is improving its technology with each passing day for more precise measurement of this cosmic phenomenon. To ensure the accuracy of data received, LIGO operates two observatories, each placed at a distance of 1900 miles. If a signal is picked by both the observatories with approximately the same intensity, then the chances of it being a gravitational wave increases.

Is there any theory based on the existence of gravitational waves that are proved or to be proven in the future?

The scientifically reliable detection of the GWs came from the detection of a black hole collision back in 2015. It was detected that two binary black holes collided and formed a massive black hole approximately 1.3 billion years ago. To be precise, the gravitational waves were detected on September 14, 2015, at 5:51 am EDT. The LIGO observatory in Livingstone detected the gravitational waves 7 milliseconds earlier than the LIGO observatory in Hanford. This provided definitive proof of Einstein’s “Theory of Relativity”. According to Einstein’s predictions, a pair of massive objects (like binary orbits of neutron stars or orbiting Black holes for instance), emit or lose their energy of rotation by emitting gravitational waves. Now, considering the case of orbiting Black holes specifically, the expulsion of energy in the form of gravitational waves is much higher, which also means that the rotational energy of the orbit decreases. As a result, a single and massive black hole is created, converting a portion of the combined black holes’ mass into energy. This notion conforms to Einstein’s formula E=mc 2 . This energy is emitted as a final strong burst of GWs. It is these gravitational waves that LIGO observed [6].

The detection was also converted into sound and made available as a video in the public domain by Caltech and MIT.

Considering Physicists success in detecting gravitational waves it is still not near to satisfy theories with full accuracy. Hence, it requires physicists and engineers to continuously develop mechanisms and technologies to address the theory of GWs.

This article discussed the fundamental knowledge on the concept, functioning, and impact of gravitational waves and their research. Gravitational-wave research is now extremely popular, especially after the first detection in 2015. Rainer Weiss, Barry Barish, and Kip Thorne were honored with the Nobel Prize in Physics for the amazing use of interferometer and converting it into inferences on one of the simplest but advanced operating mega structures on earth. Scientists look forward to analyzing even more accurate data received viz. Detections of gravitational Waves. LIGO and Virgo collaboration has proven records to have the capability to detect the gravitational waves from the “Big Bang” 13.7 billion years ago. To date, gravitational waves remain one of the strongest evidential proof scientists have found to Einstein’s theory of Relativity. Gravitational-wave research also provides an insight into the most violent, complex, and mysterious phenomena including Supernova, Magnetar [7] collisions, and Rotating Asymmetric Neutron stars. The inter Black hole collision (most probably stellar black holes) back in 2015 in the U.S. gave the first definitive proof of the existence of space-time fabric. The collision happened approximately 1.3 billion years ago and its “ripples” were detected on September 14, 2015, which also provides experimental proof establishing the fact that GWs or the “ripples” in space-time travel at the speed of light. Periodic advancements and incorporation of sophisticated techniques and technologies will help scientists in accurately measuring stellar phenomena and bring us one step closer to the ultimate detection of gravitational waves released just after the big bang which will provide evidence for the theory. The “ripples” caused after the “Big Bang” 13.7 billion years ago can now be found as evidence to support theories like the “Big Bang” and “Einstein’s theory of Relativity”. The modification of Michelson’s interferometer to the Laser Interferometer for measurement of the gravitational waves mark a great scientific advance of the modern era.

1. “Why Detect Them?”. 2020. LIGO Lab | Caltech. https://www.ligo.caltech.edu/page/why-detect-gw
2. “What Are Gravitational Waves?”. 2018. LIGO Lab | Caltech. https://www.ligo.caltech.edu/page/what-are-gw
3. “Neutron Stars”. 2018. National Geographic. https://www.nationalgeographic.com/science/space/solar-system/neutron-stars/
4. “What Is An Interferometer?”. 2020. LIGO Lab | Caltech. https://www.ligo.caltech.edu/page/what-is-interferometer
5. The mirrors are of the world’s finest quality and experimental specifications, to avoid any shortcomings to the experiment, Wolchover, Natalie. 2020. “To Make The Perfect Mirror, Physicists Confront The Mystery Of Glass”. Quanta Magazine. https://www.quantamagazine.org/to-make-the-perfect-mirror-physicists-confront-the-mystery-of-glass-20200402/
6. “Gravitational Waves Detected 100 Years After Einstein’s Prediction”. 2020. LIGO Lab | Caltech. https://www.ligo.caltech.edu/news/ligo20160211
7. Kaspi, Victoria M., and Andrei M. Beloborodov. 2017. “Magnetars”. Annual Review Of Astronomy And Astrophysics 55 (1): 261-301. doi:10.1146/annurev-astro-081915-023329.

Figure References

1. Cover Page Figure: Artistic representation of Binary Black hole system (Credit “Tidal Forces Carry The Mathematical Signature Of Gravitational Waves”. 2019. MIT Technology Review. https://www.technologyreview.com/2019/12/14/131574/tidal-forces-carry-the-mathematical-signature-of-gravitational-waves/.)
2. Figure1:Earth’s representation of Space-Time (Credit: “Could Quantum Mechanics Explain The Existence Of Spacetime?”. 2019. Discover Magazine. https://www.discovermagazine.com/the-sciences/could-quantum-mechanics-explain-the-existence-of-spacetime.)

3. Figure 2: An experiment where a ball is placed on a stretched sheet, similar to the neighboring image of Earth. (Credit: “Where Does Gravity Come From? – Universe Today”. 2013. Universe Today. https://www.universetoday.com/75705/where-does-gravity-come-from/.)

4. Figure 3: An artist’s impression of gravitational waves generated by binary neutron stars. (Credit: “NSF’S LIGO Has Detected Gravitational Waves”. 2016. NASA. https://www.nasa.gov/feature/goddard/2016/nsf-s-ligo-has-detected-gravitational-waves/.)

5. Figure 4: Ripples on the surface of water similar to that of Gravitational Waves. (Credit: “Water Ripples Free Stock Photo – Shotstash”. 2020. Shotstash. https://shotstash.com/photo/water-ripples/.).

6. Figure 5: A Diagrammatic representation of Michelson Interferometer. (Credit: “The Michelson Interferometer – A Laser Lab Alignment Guide”. 2018. Wiredsense. https://www.wiredsense.com/tutorials/the-michelson-interferometer-a-laser-lab-alignment-guide.)

7. Figure 6: A Diagrammatic representation of Laser Interferometer by LIGO. (Credit:”What Is An Interferometer?”. 2020. LIGO Lab | Caltech. https://www.ligo.caltech.edu/page/what-is-interferometer.)