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  • A Simple Study of Gravitational Waves


    Time passes and human technology takes steps towards something greater. Scientific advancement is not a steady incline but rather an inconsistent set of leaps and hindrances. Although, for our relatively short period in existence, the leaps seem to arise slowly. During our lifetime we have few chances at experiencing the evolutionary jumps of human technology but when it does it’s breathtakingly beautiful, for it opens up new ways of understanding the universe. We have experienced one of these leaps in the past few years, as the direct observation of gravitational waves. A discovery that will be held in the hands of many to come
    This will be general introduction to gravitational waves. It will cover what they are, how they're produced, their effects then the process and tools for detection. Technicalities and important theories surrounding GW as well. Lastly, the history will be shown as well as the future that GW technology holds. Additional resources are on the last page of the site: links to additional information and the works cited.

    Production and effects
    Gravitational waves are a warping of space and time which radiates at the speed of light from an accelerating mass. Much like ripples in a pond after a stone has been thrown in, but instead of a stone it's a black hole and instead of water it's the fabric of space and time. This distortion is so miniscule, a thousand times smaller than an atomic nucleus, that it's undetectable except with the most scientifically advanced equipment. Since we can study the gravitational waves radiating from a specific source it allows us to investigate distant cosmic bodies directly, which we have never before now had the capabilities.
    Gravitational waves are a rare and phenomenal occurrence in nature. Due to the nature and requirements for their creation it's incredibly difficult for noticeable GW to arise. Massive objects must be accelerating a relativistic speeds, that is to say an object moving at a speed comparable to the speed of light. GW radiators must be binary, orbiting another body of similar mass, to move at relativistic speeds. The objects must be similar in mass to neutron star: density of 1017 kg/m3 with a diameter of 10-20km, or comparable to a black hole. Although the density and size becomes a bit obscure with black holes. To put in perspective, the gravitational force of a neutron star is 10^11 (10 billion) times stronger than earth's. So obviously neutron stars and black holes are the only detectable emitters of GW. The gravitational waves will be radiating from the common center of mass between the binary bodies. It's presumably unobtainable, because of the massive components needed for gravitational waves to arise, to ever have a constant reliable human made source of GW in a laboratory.

    Observation and Tools for Detections
    Even though the direct observation of gravitational waves is a new discover GW waves as a concept has a long history dating back to the early 20th century. The first theory of gravitational waves were by Albert Einstein in his theories of general and special relativity in 1916 and 1918.
    The confirmation of this theory wasn't until 58 years later in 1974 with the Hulse-Taylor Pulsar being the first indirect observation of GW. Achieved by monitoring a pair of binary neutron stars, the first binary neutron star ever discovered. The binary star was emitting pulses of radio waves that could be measured from Earth. The intervals between these waves, after 3 decades of careful measurement and monitoring, we're found to be inconsistent. Concluding that the orbits of the neutron stars was changing meaning that energy was being lost through the emission of gravitational waves. After this discovery, many more neutron star binaries were found and studied, verifying the initial conclusion. However, the academic community was still unsure about GW emanating from black holes since their complex physical properties.
    After another four decades of nothing, came the first direct observation of a GW. The observation was achieved by the LIGO institute and team, after a 50 year effort that concluded in success on september 14th 2015. The first detection was that of a gravitational wave that had emanated from a binary black hole that quickly collapsed into a singular, larger black hole. Since then, three more GW have been observed. As we know, GW travel at the speed of light and with the understanding Einstein's field equations physicists can study the black hole or any source emitting GW in greater detail than any other method used in the modern world.
    Comically, the members of the team, upon first discovery of the wave, didn't believe the signal to be real. They accepted it as an error of method, but, after a year of careful inquiry into the signal, no errors were found and thus indicating they had actually observed a gravitational wave, excitement flourished. The discovery was announced publicly in February of 2016 and in 2017 key members of the LIGO team won the 2017 Nobel prize in Physics.

    Laser Interferometer
    The first detection of GW happens at the Laser Interferometer Gravitational-Wave Observatory (LIGO) in the U.S., using Laser Interferometry: a method for measuring distances incredibly accurately. There are two LIGO institutes in the US for higher scientific accuracy and LISA, another laser interferometer institute located in Europe. Having multiple stations in the US insured that the detection was more than an error in the instrument, since no two errors could occur simultaneously in both institutions across the country.
    The instrument is structured carefully and specifically so that they can measure distances 10^-21 meters, roughly the size of a proton. There are two 40 km long arms, perpendicular to each other, with mirrors on the ends of each. Lasers are shot down the arms via a beam splitter a come from a single source. The light travels down the arm and reflected back off the mirror, the beam splitter superimposes the light waves and sends the superimposed waves to a photodetector. The alignment of both waves causes the photodetector to measure different amounts of light, the brightness depends on whether or not the peaks and troughs cancel each other out or intensify each other.
    GW are noticeable with this method because during the distortion of space time one arm will elongate and the other shorten. Since the speed of light is finite and doesn't change, the time spent traveling will change if it's traveling in the longer arm or the shorter arm. Thus changing the alignment of light waves being detected by the photodetector. Since the warping is so miniscule the challenge is to have the instrument only detect the GW and thus all outside disturbances must be eliminated.

    Relativity
    Our understanding of gravitational waves would be nowhere without Einstein's theories of relativity along with the field equations included within. In Theory of General Relativity he proposed an alternative to newtonian gravity: gravity is not a force of attraction but instead geometry and the warping of space-time. Binary bodies have a different effect than a singular mass, rather than just warping space, they produce gravitational waves. Space-time is a measurable geometric structure thus, accompanying the theories, Einstein created his incredibly complex and astoundingly important field equations. Which are used to understand the signals being received at LIGO while also giving the tools for calculating characteristics for GW sources. i.e.the points in space and in time the event occurred; the mass and type of bodies involved; the energy contained in the wave and released during the event.
    These equations become very complex very quickly. On the surface, one may seem simple enough but each variable represents another equation that holds more variables with even more equations contained within that. Adding to the complexity, most equations are nonlinear meaning that a single input may have multiple outputs which also equate to astronomically large bodies with incomprehensible densities in places of the universe our telescopes cannot see. Nevertheless, astrophysicists can solve the field equations, although pen and paper methods are practically impossible. Modern computers, along with intricate algorithms and templates, are key to the study of gravitational waves.
    It's important to note that the primary radiators of GW, black holes and neutron stars, have fundamental characteristics that we don't understand. Black holes, for example, are not made of matter so they have the simpler calculations since some aspects of the calculations can be disregarded. Neutron stars are manyfold more complex. There is a poor understanding of matter at densities like those of neutron stars and thus making them difficult to use in the field equations.

    Space Time
    Any subject, in our case gravitational waves, relating to or incorporating either of Einstein's theories of relativity: Special or General, it's becomes crucial to understand space-time. One of Einstein's most essential additions to human scientific advancement. In General Theory of Relativity, Einstein states that space and time, are not separate entities but rather connected in a singular measurable reality called space-time. Furthermore, he adds that gravity is not a force but rather a bending of space and objects falling into the bend. Contrary to the Newtonian theory that gravity is an attractive force between two bodies with the force relative to the size of each of the body.

    The Future
    “Every time a window a window is opened in the universe, unexpected things are seen. And this will be no exception”
    -Kip S Thorne

    The most important part of the gravitational waves is not the observation itself but rather that it's now a tool to study the universe with greater sophistication than anything before. Gravitational waves will be used as a tool to study regions of space that our modern telescopes cannot penetrate and study regions of time deep in the past. Gravitational wave radiation would have been the only form of radiation that could permeate through the very hot and very dense materials in the first few seconds of the universe. If we were ever able to directly see the big bang it's through gravitational wave technology.
    The technology used to observe gravitational waves are still in their infancy so there are many developments are yet to come. Routine detection and investigation is the next step for LIGO and other institutes. Advancements include reaching further into the depths of space, accomplished with more sensitive and stable detection arms. Sensitivity is achieved with longer interferometer arms because more space is distorted relative to the length of the arm. For instance, a wave distorts a meter by 10^-21 meters, 10 meters by 10^-20 meters and so forth. Although longer distances get difficult on a planet, too many limitations, but having a laser interferometer in space has almost no limitations and lengths of arms can be a great deal longer than anything on earth.
    This magnitude of discovery occurs few times in a century and has given us the opportunity to open our eyes. A discovery that is giving us a tool to let our eyes peek into the furthest depth of the universe. Let us reach once more for the answers to the universe.