Gravitational Waves – A New Window to the Universe

Some 1.3 billion years ago, as plant life was making its first appearance on Earth, two black holes 29 and 36 times the mass of our Sun, collided.  The result of this collision was a single black hole 62 times the mass of the Sun.  The remaining mass, equal to three Suns, was expelled as energy.  This energy created a ripple in the space-time fabric referred to as gravitational waves.  These waves, which emanated from the colliding black holes like pond waves formed by a rock tossed into it, were detected by the LIGO team on September 14, 2015.  The announcement made today, culminates a 100 year effort by physicists to confirm Albert Einstein’s prediction of gravitational waves.

What are gravitational waves?

Issac Newton’s theory postulates that gravity acts as an instantaneous force throughout the universe.  That is, the gravitational force from the Sun, Earth, even your body, is felt immediately on every other body everywhere.  As Einstein worked up his theory of relativity, he knew there was a problem with this.  According to relativity, there is a firm speed limit in the universe, this limit being the speed of light.  As nothing, whether it is matter or energy, could travel faster than this, it would not be possible for the effect of gravity to travel faster than light as well.  Clearly, a new way of explaining gravity was required.

Einstein found this explanation in the form of gravitational waves.  If there was to be some sort of perturbation in the Sun’s gravitational field, we would not sense it right away on Earth.  Instead, the disturbance would radiate from the Sun at the speed of light in the form of gravitational waves.  It takes light eight minutes to reach Earth.  Thus, a time lag of eight minutes would occur before we would feel the gravitational disturbance on Earth.  In the same manner, there was a 1.3 billion year lag to detect the gravitational waves from colliding black holes located 1.3 billion light years away.  Had Newton’s theory of gravity been correct, the gravitational effect of the colliding black holes, however faint, would have reached Earth instantly 1.3 billion years ago rather than last September.

I want to emphasize that Newton’s theory of gravity works in most situations.  Newton’s predictions deviate from Einstein’s predictions in two key situations.  One is when a body is located very close to a large mass, such as Mercury is to the Sun.  The other is when a body is traveling near the speed of light.  In other situations, Newton’s and Einstein’s equations yield the same result.  In fact, NASA engineers will use Newton’s version of gravity when they can as it is easier to work with than relativity.  The Apollo program, for example, sent humans to the Moon using Newton as a guide.  Replicating Newton’s results where they are accurate was a key stepping stone for Einstein when devising relativity theory.

Another key stepping stone for relativity was making successful predictions where Newton could not.  One such example is the orbit of Mercury.  The perihelion (spot closest the Sun) of Mercury’s orbit advances 43 seconds of arc per century (43/3600th of a degree) more than predicted by Newton.  This advance is visualized in exaggerated form below.

Credit: Wikipedia/Rainer Zenz

When Einstein found out that his theory’s solutions predicted Mercury’s orbit perfectly, he was so excited he experienced heart palpitations.  As opposed to being a force, general relativity views gravity as a bending of space-time.

As an object bends the space around it, another object will travel along the path of that curvature.  Also, electromagnetic radiation such as light will follow the curvature as well.  If an object accelerates, as when happens when black holes are colliding, it will generate ripples in space time.  And it is these ripples that LIGO detected.

The universe is not very pliable and it took a tremendous amount of energy to create these waves which are very small, only 1/1000th the size of a atomic nucleus.  How much energy?  Matter in the amount of 3 solar masses was converted into energy in the collision.  Using Einstein’s famous equation:

E = mc²

E = 3(1.99 x 10³⁰ kg)(3.0 x 10⁸ m/s)²

E = 1.79 x 10³⁹ J  where J = Joules

The Hiroshima atomic bomb released about 10¹⁴ J of energy.  This means the black hole collision detected by LIGO released 1.79 x 10²⁵ times the amount of energy as the 1945 atomic bomb.  When you see the amount of energy involved, and how small the gravitational waves detected were, its easy to understand how difficult it is to observe these waves.  In fact, Einstein was doubtful gravitational waves could ever be detected as they are so faint.  The announcement today is a result of an effort started in the 1980’s to build the LIGO facility.

In 1992, the NSF granted funding for the LIGO project to commence.  It consists of two facilities, one in Livingston, LA, and the other in Hanford, WA.  As a sidenote, Hanford was the site of a key plutonium production plant during the Manhattan project.  Each facility has two 4 km tubes where a laser is sent through.  The mirrors in the interferometer are calibrated so when the two light beams reach their final destination, they cancel each other out so no light is recorded at the photodetector.  This is known as destructive interference and is pictured below.

If a gravity wave passes through LIGO, the ripple in space-time moves the mirrors just enough to cause the laser to captured by the photodetector.  This movement is much too slight to be felt by humans and thus the need for sophisticated equipment to catch it.

LIGO has been operational since 2002.  During its first run, no gravitational waves were detected.  LIGO underwent a recent $220 million overhaul to increase its sensitivity.  As mentioned in the press conference today, LIGO is only at a third of its final expected resolution capability.  This bodes very well for more discoveries at LIGO over the next decade.  In all, LIGO has cost $650 million since its inception in 1992.  That is 1/10th the cost to rebuild the San Francisco-Oakland Bay Bridge.  This discovery has the potential to open a new window of observation for astronomers.

To the general public, astronomy for the most part means the classic image of an astronomer peering through an optical telescope or the famous imagery from the Hubble Space Telescope.  What is not as well known are telescopes that observe other forms of radiation.  This includes Earth-bound radio telescopes and space telescopes such as the infrared Spitzer Space Telescope and the Chandra X-ray Observatory.  Why bother with these other forms of radiation?  Think of it this way, imagine a tower located a mile away on a foggy day.  The tower has both a light beacon and radio transmitter.  The fog blocks out the light, making it invisible.  However, if you have a radio receiver, you’ll be able to pick up the radio transmission as fog is transparent to radio waves.  In this manner, astronomers use different types of radiation to detect objects not visible in the optical range.

Besides the continuing upgrade at LIGO, there are future gravitational wave observatories anticipated in India, Japan, and it is hoped, in space.  Today’s result overcomes the most important hurdle.  When LIGO was funded, many scientists were skeptical it could actually detect gravitational waves.  Now that we know it can be done, that clears a major obstacle for funding.  The opening of the radio window allowed the discoveries of pulsars and the cosmic microwave background radiation.  The x-ray window allowed us to view accretion disks around black holes.  The next decade should provide us with additional surprises about the universe as the gravitational wave window opens up.

Above is the LIGO gravitational wave detection result announced today.  The strain is the distance space-time was stretched during the event.  At 10^-21 m this is, as mentioned before, about 1/1000th the size of an atomic nucleus.  What gives the LIGO team confidence this is not a false detection as the one produced by the BICEP team two years ago is the gravitational wave was detected by both the Livingston and Hanford observatories.  You’ll also note how closely the observed wave matches with the predicted wave.  The hallmark of progress in science is when theoretical prediction matches observation.  If Einstein were around to see this, I suspect he may have had heart palpitations just as when he found a match between relativity and the orbit of Mercury 100 years ago.

*Image on top of post displays how the colliding black holes produced the gravitational waves discovered by LIGO.  Credit:  Credit: LIGO, NSF, Aurore Simonnet (Sonoma State U.)