Last Updated 04 Jan 2023

Investigation Related To Gravitational Waves

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Introduction

When looking up at the night sky, preferably on an unclouded night away from the corpulence of light pollution, one sees stars. With the unaided eye, one can perhaps see a few thousand stars dazzling in the night. That does not mean there are necessarily only a few thousand stars in the whole universe. In fact, the reader has an implicit knowledge that the number of stars in the universe must exceed this, whether from past learning or intuition combined with past learning. The number does exceed a few thousand for sure. With the aid of telescopes, below our atmosphere and above, a whole new world is literally illumined to us. For example, the Hubble space telescope in orbit of Earth has provided imagery for astronomers to garner that the number of stars is somewhere around 1023.1

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Telescopes not only help us to see objects in the universe, like the aforementioned plethora of stars; but also help us to look farther back in time. Light, electromagnetic radiation, in its varying spectra, is received by our telescopes so that we are able to see objects far away and in the distant past. Electromagnetic radiation can only take us as far back as detectable however. For example, the cosmic microwave background is the “oldest” light in the universe, in which we detect the earliest stages of the universe. The classic image of the astronomer peering into a telescope stops here it seems. However, electromagnetic radiation is not the only tool offered to scientists studying the universe. Gravitational waves take us possibly further, ushering in a new age for physics and astronomy.

Gravitational Waves

Albert Einstein, one of the foremost physicists of the past century, formulated his General Theory of Relativity in 1915. From this theory, the existence of gravitational waves is mathematically derived.2 Einstein’s formulation of his breakthrough theory involved describing gravity as a geometric property of spacetime. Spacetime, geometrically speaking, is four dimensions: the three we ourselves move in (xyz) and the fourth included being time (the change we experience). Since gravity is so intimately connected with spacetime, one can understand gravitational waves simply as ripples or perturbations through spacetime. An object with mass, and hence a gravitational force attributed to it, will disturb spacetime and cause wavelike ripples. It can be analogously understood by your disturbance of water when you swim through a pool—the spacetime fabric, water in this case, is disturbed by an object with mass, your swimming, causing waves to emanate forth. These gravitational waves, caused by objects with mass, can also affect objects with mass, making them squeeze and stretch as waves pass through them—like a spring. Below is a figure depicting a mass distorting a 2D representation of spacetime.

3 Binary Pulsars Discovered

Einstein’s theory of General Relativity would take scientists on a 100 year long odyssey, from mathematical formulations, to the space age discovery of binary pulsars, and ultimately to the experimental detection of gravitational waves. Setting off to the space age, we see the discovery of a binary pulsar system. This turned out to be a major stride on the path to confirming the existenceof gravitational waves. “Taylor and Russell Hulse discovered in 1974 a binary system composed of a pulsar in orbit around a neutron star. Taylor and Joel M. Weisberg in 1982 found that the orbit of the pulsar was slowly shrinking over time because of the release of energy in the form of gravitational waves. For discovering the pulsar and showing that it would make possible this particular gravitational wave measurement, Hulse and Taylor were awarded the Nobel Prize in Physics in 1993.”

The two astronomers followed the mathematical derivations of gravitational waves, as laid out in General Relativity, and found their observations of the pulsars to be consistent with that of General Relativity’s proposals. To describe the concept: binary pulsars are high-density stars which orbit each other with high speed, and consequently, high energy. This high speed provides an emission of gravitational waves at a sufficiently high rate, where the two astronomers were able to observe over the course of many years that they were slowly getting closer to each other. This loss of energy and the amount lost is consistent with the mathematical formulations of Einstein’s Relativity. Below is the differential equation describing radial decay of a binary system.

dr dt = −64 5 G3 c5 (m1m2)(m1 + m2) r3

This differential equation describes the decay with time of a binary system collapsing on itself. This equation was used to describe the rate of decay of the binary pulsar system. The results were then compared to Einstein’s formulation of gravitational waves and their prescribed energy; to which the results coincided together almost perfectly. r is the distance between the two objects, t is the time, c is the speed of light, G is the gravitational constant. Solving the differential equation yields the time it takes for the binary to collapse in on itself.

t = 5 256 c5 G3 r4 (m1m2)(m1 + m2)

Detection

Detection of gravitational waves is no easy task. One can easily perceive visible light with their eyes, or use instrumentation to survey astronomical phenomena far away (cosmic microwave background). It is a whole other task to detect gravitational waves, mainly because their effects are so miniscule on the objects around us. However, as is seen with the binary pulsars described above, or with other similarly high-density/massive objects like black holes orbiting each other, gravitational waves are detectable with the instrumentation in use today. This leads us to the Laser Interferometer Gravitational-Wave Observatory (or LIGO), which successfully detected gravitational waves for the first time in 20154.

This instrument, far from a telescope, consists of two orthogonal long tubes, each four kilometers long, a laser interferometer at the origin, and two suspended mirrors. Since gravitational waves perturb spacetime, and subsequently objects which bend and stretch from this distortion, LIGO is the perfect instrument to detect sufficiently large gravitational waves. If any gravitational wave passes the detector, the arms of LIGO should stretch and the laser interferometers should detect that light was received at the origin of the detector and not cancelled out. If the light pulse sent through the two arms reflected back from the ends of the arms to the origin, the waves would cancel and thus gravitational waves would not be detected. But, the waves did not cancel in the historic moment of 2015, and instead the arms were indeed perturbed. Below is an excellent representation of LIGO5 provided by the LIGO team.

Conclusion

The century-long odyssey, from theory to detection, is an excellent feat of scientific triumph and human ingenuity. The significance of which heralds in a new frontier for physics. Just as the famous Star Trek opening goes, “Space, the final frontier. . . ”; we can similarly say, “Spacetime, the new frontier. . . ” Thats to say, gravitational wave astronomy/physics is a new and bustling field. It opens up new avenues of understanding the early universe, possibly even beyond what can be observed by mere electromagnetic waves.4

References

European Space Agency, Website URL https://www.esa.int/Our_Activities/Space_Science/Herschel/How_many_stars_are_there_in_the_Universe
Laser Interferometer Gravitational-Wave Observatory, Website URL,https://www.ligo.caltech.edu/page/what-are-gw, Operated by Caltech and MIT
Laser Interferometer Gravitational-Wave Observatory, Website URL,https://www.ligo.caltech.edu/news/ligo20160211, Operated by Caltech and MIT
Edwin F. Taylor and John Archibald Wheeler, Exploring Black Holes: An Introduction to General Relativity, Publisher: Addison Wesley Longman; 1 edition (July 22, 2000), Chapter 16
LIGO Multimedia Archives, https://www.ligo.org/multimedia.php

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