Gravitational Waves

Image courtesy of https://www.sciencenews.org/blog/context/gravity-waves-exemplify-power-intelligent-equations

What’s a Gravitational Wave???

A great explanation of gravitational waves comes from a book dedicated to the topic. It is called “Gravity’s Shadow: The Search for Gravitational Waves” by Harry Collins. The book is lengthy, but contains an enormous amount of information about the history of gravitational wave detection (here is a copy of the book: Gravity’s Shadow). A great explanation from this work, and one that I will tweak, goes as such:

Personally created image

Imagine a planet orbiting it’s parent star. Let’s not worry much about the shape of the orbit or any other details than the attraction the planet feels from it’s parent star. The planet and star are locked in the embrace they have been for millions of years. All is well until suddenly, the star is split into pieces. Some pieces go flying off in directions perpendicular to the plane of the planet’s orbit. But the largest piece remains in the original position of the star.

Personally created image. Please ignore any errors in star placement. This is just an analogy. Let's image the star is still in the center of the planet's orbit.
Please ignore any errors in star placement. This is just an analogy. Let’s imagine the star is still in the center of the planet’s orbit.

We know that space-time curvature is what keeps the planet orbiting the star. But with the decreases mass of the star we have decreased curvature. The orbit of the planet will definitely be altered, and become more distance from the star. But when does the planet find this out? Will it instantaneously alter orbit?

General Relativity tells us that nothing can go faster than the speed of light. The planet will receive information about this change in the star’s mass no faster than a photon can carry it. If the imaginary planet-star system is Sol (our Sun) and Earth, we would not know something was amiss for 8 minutes and 20 seconds. Photons and something called gravitational waves will arrive from this now-smaller star.

Gravitational Waves are the information carriers of changes in gravitational fields, just as photons carry electromagnetic information. If there is no change in the mass of an object, then there should be no message to send. Imagine the ever popular view of curved space-time as a sheet flexible sheet.

Image courtesy of http://midhul.blogspot.com/

The star (or massive object) presses “down” on space-time, causing the curvature that the planet follows. When the mass of the star changes, this causes the curvature to lessen. Imagine taking a sheet of rubber with a weight in the middle. Now, remove the weight, and watch this change ripple outward to the rest of the sheet. Gravitational waves are, in my words, “ripples upon the fabric of space-time, caused by the interactions of very massive objects”. A wave upon the ocean effects the spacing of the water molecules. A wave upon space-time effects the very substance upon which matter rests.


Losing Orbital Energy

When an object has a stable orbit around another, there is something important to remember. The object is still being pulled by the gravity of the body it orbits. But, the object is moving in relation to this body, so much so that for a circular orbit the velocity of the object equals the force pulling it towards the body. See the below picture for clarification:

In the above, the force of gravity and the velocity of the rocket are equal. What this does is gives a trajectory somewhere between the two arrows. Image courtesy of myself and Microsoft Paint
In the above, the force of gravity and the velocity of the rocket are equal. What this does is gives a trajectory somewhere between the two arrows.

It is true that for higher energy orbits, these two arrows won’t always be equal. But for this explanation I will only consider circular orbits. In order to decay this orbit to the point of eventual collision with the body, the rocket needs to lose energy. How do we do this? Turning the rocket’s motor in the direction of the velocity, and firing away!

The rocket loses energy by thrusting in the direction of it's orbital velocity, decreasing it. At a certain point, the gravitational arrow will be larger. The rocket (provided it's landing gear situation) is doomed!
The rocket loses energy by thrusting in the direction of it’s orbital velocity, decreasing it. At a certain point, the gravitational arrow will be larger. The rocket (provided it’s landing gear situation) is doomed!

So the rocket has to lost energy to collide with the planet. This page is under the menu “Black Holes”, so how does all of this affect black holes?

It has everything to do with loss of energy. Black holes, despite the claim that they pull in everything, do lose energy in the form of something called Hawking Radiation (I won’t go into that here). When objects go into decaying orbits, and as I explained earlier, they must lose energy somehow. But Hawking Radiation does not account for the energy loss needed for two black holes to merge. Nor does it occur on the proper time span to be of any use in orbital capture. In fact, Hawking radiation is energy loss from the black holes mass. The black holes need to lose some kinetic energy to merge.

Black holes lose this energy in the form of gravitational waves. Black holes aren’t anchored in space either. They move just as every object in the universe does, and sometimes are swallowed by other, more massive black holes.


A great explanation

Check the video below for a great visual:

(PLEASE SEE “BLACK HOLES IMAGE RESOURCES” PAGE FOR VIDEO SOURCE)


DETECTING GRAVITATIONAL WAVES

Image courtesy of http://www.pbs.org/wgbh/nova/next/physics/advanced-ligo/

I didn’t feel a thing!

So, we are to believe that gravitational waves are all around us? Passing through everything we see? Why don’t we feel them? Gravitational waves, even ones caused by massive objects such as black holes, are stretches in space-time that occur at subatomic distances. Evolution really doesn’t care enough about this kind of spacing to have given us an apparatus to perceive changes in it. To us, organisms made of matter, nothing happens at all.

How do we see such things if they are so small? If you watched the video on the previous page “Gravitational Waves”, then you saw that any physical apparatus (a ruler, for example) can’t be used to detect these waves, since the ruler itself will be stretched and compressed. But, as we saw, the speed of light is one tool we can use to measure the passage of a gravitational wave.

In walks LIGO, the structures depicted in the above image. LIGO stands for Laser Interferometer Gravitational-Wave Observatory. It consists of two locations: one in Hanford, WA and another in Livingston, LA. There is an excellent website by Caltech (the operator of the apparatus) here. LIGO can measure on the scale of the distances needed for gravitational wave detection using a technique called interferometry. Interferometry uses properties of laser beams to note very small displacements.

Image courtesy of https://www.sciencenews.org/article/gravitational-waves-explained. Each detector arm is 4 kilometers long. Remember, we are looking for very small shifts in the length of the detectors. So a long detector arm is needed, to allow the light longer to transit.

To put it simply, the LIGO detector sends a laser beam out through a splitter. This beams then go down the detector arms to two mirrors, and are reflected. After recombination they are sent to a detector. If the waves arrive back totally in phase with one another, then there is no change in the distance of detector arms. But if they arrive back out of phase, this signals that the length of the detector arms have changed. As we saw on the previous page.  happened is for the space the detector arms occupies changes

Waves in phase will show no change in the light received. Waves totally out of phase will cancel each other, leaving dark spots. Waves slightly out of phase will register somewhere in between.

Some issues that LIGO has faced in the past is noise. Noise, in this case, is in the form of vibrations in the ground that can shake the mirrors (which hang very delicately from the tunnel). Anything from seismic activity to a passing train can affect the detector. Such things must be accounted for, and nulled out as much as possible, for optimal detection.


Success!!!

There is little doubt that you have at least heard of the recent news from LIGO, that gravitational waves were actually detected by the apparatus! On September 14, 2015 both of the LIGO detectors picked up signals from somewhere in the universe. It is believed that the signal was produced by the merging of two black holes.

(PLEASE SEE “BLACK HOLES IMAGE RESOURCES” PAGE FOR VIDEO SOURCE)