  #### How Fast Is It - 06 Gravitational Waves (1080p)

by: David Butler

##### Transcript:

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at the end of the second segment on general relativity I pointed out that Einsteins prediction that accelerating masses can create gravitational waves had yet to be discovered as soon as I released the book they were discovered so I have added this chapter to the video book to go into gravitational waves what they are what is a ripple in space-time what creates them what can create a gravitational wave large enough for us to detect and how did we actually detect it now we used interferometers the Michelson interferometer to actually detect the first gravitational wave I'll end by discussing the impact on cosmology that the discovery of gravitational waves means but first what is a ripple in space-time here on earth far from an event that could create a gravitational wave we have a relatively flat space with Euclidean metric G that isn't changing with time a ripple represents small deviations from this flat space-time metric we use H to represent these deviations solutions to Einstein's equations show that a gravitational waves metric oscillates sinusoidal e just like light and it travels at the same speed as light as a wave moves down the z axis planes at different times experience different values for the metric used to measure distance on the plane this makes the wave a transfer sway just like light we see two possible polarizations for a gravitational wave we call one h+ for the action along the x and y axis we call the other h cross for action along the diagonal to see what an oscillating H+ metric does we'll measure the changes in the distance between two points on the plane when a gravitational wave passes here we have an XY plane with the wave passing into the page we mark two points on the x axis one meter apart in Euclidean flat space where H is zero when H is greater than zero the distance between the two points on the x axis become longer than one meter by an amount equal to H times the original distance at the same time a one meter distance on the y axis will shrink to less than one meter by the same amount when H returns to zero the distance between these points returns to one meter when H is less than zero the distance between the two points on the x-axis will become shorter than 1 meter and the distance between the two points in the y-axis will become longer than 1 meter here's an exaggerated look at what an oscillating h plus polarized gravitational wave does to a square plate it passes through again the wave is passing into the page for an H cross polarized wave the effect would be similar but shifted 45 degrees when describing a gravitational wave we can now be more precise than its a ripple in space-time a gravitational wave is an oscillating polarized metric that operates in the plane perpendicular to the direction of the wave as it moves through space at the speed of light and we have seen what this means for the objects that encounter such a wave they are stretched and squeezed in various directions will now turn our attention to the kinds of massive accelerating objects that can create such a wave in order to generate a gravitational wave you need a non spherically symmetric rotating system for example here's a binary star system with two masses revolving in a circular orbit around a common center of gravity the Stars acceleration creates gravitational radiation that travels out from the system in all directions just like the light they are generating the gravitational wave solutions show that the frequency of the created gravitational wave is twice the rotation rate of the binary system we also see that the polarization and maximum gravitational wave amplitude depend on the masses of the two objects the distance between them their rotational velocity the viewing angle and how far away the system is from the observer

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there is one more key factor to consider when it comes to binary systems namely that the gravitational waves carry energy and momentum away from the system we call as gravitational luminosity Newton and Kepler provided the mechanics for understanding what happens to the orbit when gravitational energy is lost because binding energy is negative a loss of energy will make it a larger negative this has the effect of reducing the distance between the two objects this in turn increases their velocity a shorter circumference and faster velocity reduces the time it takes for a full orbit and therefore increases the frequency of rotation and therefore the frequency of the gravitational wave and the wave equations show that the amplitude of the gravitational wave will increase with the frequency the rate that the frequency is changing is called the chirp it gives us the ability to express the amplitude of the gravitational wave in terms of the frequency and the rate the frequency is changing instead of the masses and the distance between the masses this is crucial because for most cases we will have no way of knowing directly what the masses are or how far apart they are but measuring the frequencies might be possible if we can also measure the amplitude we can even calculate the distance to the binary system because this distance is based on gravitational wave luminosity it is called the luminosity distance for most all gravitational wave sources this will be the only way to figure out how far away they are

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this plot combines the data from both sites the waveform is consistent with coalescing masses with a 10 cycle 200 millisecond Inspiral that gives us the frequency the rate of change of the frequency and a peak wave amplitude a merger that takes around 2 milliseconds and a ring down as the coalesced objects cease to radiate gravitational energy detector noise introduces errors into all the calculations based on these figures that's why we'll provide a range for each item the amplitude and frequency data points give us the luminosity distance it is important to note the gravitational waves experienced redshifting as they travel across the cosmos just like light does having traveled around a billion light years this wave would have experienced a redshift near 0.1 so the frequency we see here is a bit smaller than the frequency at the start of the waves journey here the frequency data also gives us the chirp mass taking the redshift information gleaned from the merger and ring down portions of the wave form we get the binary system masses these masses are too large for neutron stars that are only a few times the mass of the Sun so we must be witnessing the merger of two large stellar black holes

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during the last 200 milliseconds of their in spiral the orbiting velocity of the black holes increased from 30 percent the speed of light to 60 percent of the speed of light over the same period the distance between the two black holes went from around a thousand kilometers to just under 200 kilometers when their event horizons made contact modeling the final ring down shows that the mass of the resulting curb Lac hole is around 62 solar masses that's three solar masses less than the sum of the masses of the two in spiraling black holes this mass was converted to the radiated gravitational energy in other words during the final 20 milliseconds of the merger the power of the radiated gravitational waves peaked at about three point six times ten to the 49th watts let's take a second to get a feel for how large this number is in our how far away is its segment on nearby stars we found that the Sun converts four point two six metric tons of matter into energy every second the resulting power output is equal to four billion hydrogen bombs exploding every second the Sun is an average star so we can use this as an average stellar power output from our segment on local superclusters we saw that there are 250,000 trillion stars within 1 billion light years is represented around 7 percent of the total number of stars in the universe we get the total power emitted by all the stars in the visible universe by multiplying the average watts per star times the number of stars the power generated by this merger of the two stellar-mass black holes is 26 thousand times greater than the combined power of all the light radiated by all the stars in the that's the signal we saw in September 2015 a billion years after it happened

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the wave information does not tell us in which direction it came from because each interferometer is a whole sky monitor with very little directional information and having two detectors does give us some directional data for example if the wave came in parallel to the line between the two sites the signals would have registered at the exact same time if the wave was perpendicular to the line we would have seen a time delay of 10 milliseconds because the wave travels 3002 kilometers through the earth at the speed of light what we detected was a wave that came in at an angle that caused delay of 6.9 milliseconds the dotted line represents the distance the wave had to travel for a piece of it to reach the hanford interferometer a little trigonometry gives us the angle of course this angle gives us a circle of possible directions

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interferometers are most sensitive to waves that come in perpendicular to their two arms sensitivity drops off as the incidence Direction departs from the perpendicular the curvature of the earth gives the two LIGO interferometer x' an angle difference of around 27 degrees this creates slight amplitude and phase inconsistencies across the two detectors that enable a narrowing of the probabilities to a smaller portion of the sky here are the most probable directions as seen from Earth the best way to increase the accuracy of our directional findings is to use a third gravitational wave detector to triangulate the source several are under construction or being upgraded to do just that here is a map of current and future gravitational wave observatory x' on the Earth's surface one of the greatest opportunities we have now that we can detect gravitational waves will be the ability to observe events that happen before light was traveling across the cosmos the first 380,000 years after the Big Bang are known as the dark ages as you can imagine there is a lot of guess work that goes into figuring out what happened during that period in the universe's history gravitational waves created within the dark ages may help us untangle that mystery more

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