The figure shows data reported to represent the first detection of gravitational
ID: 3278484 • Letter: T
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The figure shows data reported to represent the first detection of gravitational radiation using the Laser Interferometer Gravitational-wave Observatory (LIGO) detectors at Hanford, Washington USA and Livingston, Louisiana USA. The interferometers each consist of two orthogonal arms along which laser beams propagate, are reflected, and then interfere at the vertex. The measurement is the strain induced in the interferometer by the passage of gravitational radiation. Analysis of these data is claimed to represent the merger of two orbiting black holes, each of approximately 30 solar masses . Describe, analyze and critique the data presented in the figure. Using complete English-language sentences explain the features and information content of this figure leading to the conclusion that LIGO has detected gravitational radiation. Write up to 15 sentences.
LIGO Hanford Data redicted 1.0 O 0.5 c 0.0 g -0.5 LIGO Livingston Data Predicted 1.0 O 0.5 c 0.0 g -0.5 LIGO Hanford Data (shifted) 1.0 O 0.5 c 0.0 C -0.5 LIGO Livingston Data 0.30 0.35 0.40 0.45 Time (sec)Explanation / Answer
First of all to discuss these data we have to understand the fundamentals. The coming wave from the blackhole binaries was sensed via the feature of the wave. The wave had the capacity to stress the space in one part of 10^21.
That means the coming wave can expand and contract the earth by 10^-5 of a nanometer which is approximately equal to the width of the atomic nucleaus. The observation from this two observatory points tried to test the Eienstien's general theoory of relativity as well as the famous formula E=MC^2
The two obeservatory points in Livingstone and Handford who are nearly 3002 km apart used L shaped interferometes where the mirrors in the arms is used for resonance cavity. The distance is crucial in this case as the sensitive interferometers can detect tiniest vibrations.
However, in those mirrors the wave can move back and forth creating pitch rings untill the beams overlap while the arms meet. Comparing the relative length of the interferometer arms the sensitivity of the wave can determine the prsence of gravitational wave.
Now lets get back to the diagrams.
On 14th september the wave detected by the two observatory points 3002 km away had the same wavelength nearly equal to the distance between the two points.
Now the detected large wavelength according to the numerical relativity (we consider the case of both signal and noise) can indicate the ampitude and phase of the detected wave. That means the basic parameters of the wave can be identified in the process. In both cases of Livingstone and Handford the wave shows result greater than 5 sigma standard which means the back and forth movement was more than 3.5 million times. To be precise the numerical relatvity in this case gives a value nearly 5.1sigma.
The frequency range is crucial and the disappearing time too. We get 35hz to 250hz in .25 sec. In the last diagram there is a shift which was .0007 sec that is due to the distance between the two observatory and determines a light speed wave movement. From the numerical relativity this light wave speed determines component masses 36 and 29 times greater than sun. This is only can be blackhole binaries. Moreover, in the back and forth movement in between the 4km long interferometer arms the unequality leaks the light out from the dark port. From the both observatory data it is clear that no distortion and distortion are similar to the streching and squeezing feature of wave. That means per Eienstine the radiation from the binaries strech the space in one and squeez in normal direction meets the feature of this wave detected in both cases. Therefore, it must be gravitational waves from the blackhole binaries.The shifted value exactly conforms the 3002 km distance.
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