Understanding gravitational waves: Ripples in spacetime explained

by | Aug 15, 2023

The universe is ringing with gravity, but humanity is only just beginning to hear the nuance of this cosmic symphony.
Gravitational waves abstract image.

For over 100 years, scientists have understood that the Universe is humming a symphony of gravitational waves, tiny ripples in spacetime first predicted as part of Albert Einstein’s 1915 theory of general relativity. 

However, it is only this year that the true nuance of these gravitational waves has begun to emerge, with humanity finally “hearing” the more suitable notes of low-frequency cosmic instruments under the bombast of the most violent events imaginable. Gravitational waves remained purely hypothetical until almost 20 years after the death of Einstein.  The first tantalizing hints of the existence of gravitational waves came in 1974 from observations of a binary pulsar — two neutron stars spinning around each other, blasting out radiation.  

Astronomers Russell Hulse and Joseph Taylor used the Arecibo Radio Observatory in Puerto Rico to discover that this system was changing in the same that such a binary pulsar would if it were emitting gravitational waves. The discovery would earn the duo the 1993 Nobel Prize in Physics, but it would be another 22 years before the first direct evidence of gravitational waves manifested. 

The first gravitational waves detected by LIGO

On September 14, 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO)detected gravitational waves for the first time. The source was colliding black holes located 1.3 billion light years from Earth.

Since then, LIGO, which is located in U.S., Virgo, a gravitational wave detector in Italy, and Japan’s Kamioka Gravitational Wave Detector (KAGRA) have detected gravitational wave signals from other merging black holes, colliding neutron stars, and even “mixed mergers” in which a neutron star and a black hole slam into each other. 

Yet, by detecting these gravitational wave signals, LIGO and its fellow detectors had only observed a tiny fraction of the gravitational waves that fill the Universe. Think of this as listening to a piece of music and only hearing the crash of symbols.

Detecting background under the noise

In addition to these high-frequency gravitational waves, the Universe ripples with music from less “extreme” events than the smash-up between black holes. This was exemplified this year on June 28 when the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) revealed the detection of low-frequency gravitational waves likely emerging from binary supermassive black holes in the early Universe. 

NANOgrav uses the fact that pulsars as rapidly spinning neutron stars blast out electromagnetic radiation that sweeps over Earth at incredibly regularly intervals of time, which makes them useful for keeping time. Particularly large groups of pulsars can be used to highlight changes in time cause by the squashing and squeezing of spacetime by  gravitational waves as they pas over them.

Finally, humanity had heard another player in this cosmic orchestra that uses the very fabric of space and time as its instruments, perhaps the more mellow melody of the string section that underlies the crash of symbols caused by black holes slamming into each other. Yet, there is much more to this celestial music yet unheard, and some members of this orchestra have been playing their instruments since the dawn of time.

What are gravitational waves?

In 1915, Einstein’s theory of general relativity completely changed the picture physicists had of space and time. Ten years earlier, Einstein had used a unified four-dimensional entity of space and time as the foundation of his theory of general relativity, but general relativity would take this concept much further.

Also called the geometric theory of gravity, general relativity posited that spacetime isn’t simply the stage on which the events of the Universe play out, as Newton had suggested, but is, in fact, a dynamic player in cosmic events. 

This is because an object with mass placed in spacetime causes a “warp” in this cosmic fabric. This effect can be pictured as weights of increasing mass placed on a stretched rubber sheet. The greater the mass, the larger the dent in the sheet the weight creates, and the greater the mass of a cosmic object, the more extreme the warp in spacetime it gives rise to. Gravity arises from this warping and gets stronger as the extent of the warp increases.

As physicist John Wheeler once said: “Spacetime tells matter how to move; matter tells spacetime how to curve.”

More than this, general relativity also predicted that when objects with mass accelerate, they should cause ripples that spread through spacetime at the speed of light, called gravitational waves.

The effect of a gravitational wave emission would be negligible for objects with very little mass, such as a cyclist accelerating here on Earth, but not so for massive bodies, like neutron stars and black holes or for the collapse of stars in supernova explosions. The process of continuous gravitational wave emission from binary objects has actually been an important one in the evolution of the Universe.

To see why this is, picture two neutron stars — stellar remnants created when massive stars collapse at the end of their lives — orbiting around each other in a binary system. Circular motion represents a constant change in direction, and as direction is a component of velocity, that means constantly changing velocity — acceleration. 

As the stellar remains accelerate around each other, they constantly emit gravitational waves, which we know must carry energy. The energy carried away from the binary neutron stars is supplied by the system’s angular momentum. As a consequence of the loss of angular momentum, the neutron stars move closer together, but the closer they are, the more rapidly they emit continuous gravitational waves, thus speeding up the leeching of angular momentum. 

Eventually, the neutron stars collide and merge, causing a burst of high-frequency gravitational waves. These are the gravitational wave signals that the LIGO, Virgo, and KAGWA collaboration began collecting in 2015, but as sensitive as these detectors are, they can’t hear every ripple ringing through spacetime.

What produces gravitational waves at different frequencies?

Gravitational waves are essentially the radiation of gravity, and we are no strangers to the idea of radiation having differing wavelengths and frequencies. 

The form of radiation that we are most aware of is electromagnetic radiation, in which differing frequencies give rise to radio waves, X-rays, gamma-rays, and the visible light spectrum, the latter of which our eyes have evolved to see. Just like electromagnetic radiation, gravitational waves come in a range of frequencies, wavelengths, and energies. 

Wavelength is the measure between one peak to the next in a wave, while frequency is the time it takes from one peak passing a set point to the next peak passing the same point. That means that wavelength and frequency are inversely proportional — long wavelength waves have low frequencies and low energy too, while short wavelength waves have high-frequencies and high energy.

The range of wavelengths and frequencies of gravitational waves is truly extraordinary. 

At one end of the scale, shortwave gravitational waves have wavelengths of a few miles and frequencies of just milliseconds. At the opposite end, longwave gravitational waves have wavelengths equivalent to around 110 million light-years, about the width of the Virgo Supercluster — a collection of galaxies that includes the Milky Way — with a frequency that is equivalent to the age of the Universe, around 13.8 billion years. 

Just as is the case with electromagnetic radiation, these characteristics of gravitational waves can tell scientists a great deal about their sources.

The highest frequency shortwave length gravitational waves are created as a burst when massive stars die in supernova explosions emerging from the accelerating collapse of their stellar core that can leave behind a black hole or a neutron star stellar remnant.

Slightly longer wavelength and lower frequency ripples in spacetime are created continuously by tiny bumps on the surface of young neutron stars called pulsars that are spinning as fast as 700 times per second.

Binary systems comprised of neutron stars and black holes that spiral together and merge emit continuous gravitational waves and gravitational wave bursts with wavelengths of a few thousand miles, about the width of Earth, to a few billion miles, equivalent to around the distance between the Sun and Pluto. 

Supermassive black holes that exist at the center of galaxies are occasionally accompanied by other supermassive black holes in binary systems on a whole new level that also spiral together and merge. During this process, they give rise to high-frequency gravitational waves, which lose energy and thus become low-frequency and long-wavelength gravitational waves over the billions of years they take to reach Earth and wash over the planet. 

By the time we can “hear” these ripples in spacetime, they have wavelengths equivalent to a few tens of millions of miles, akin to the distance between Earth and the Sun (93 million miles) to a few trillion miles, equivalent to around the distance between the Sun and neighboring star, Alpha Centauri (25 trillion miles). 

The source of gravitational waves with the longest wavelengths and the lowest frequency is the Big Bang, the period of rapid inflation that occurred at the very beginning of time. These are known as primordial gravitational waves or the “Stochastic Background” and result from quantum fluctuations in the hot, dense “soup” that filled the infant Universe, which are amplified by its initial bout of inflation.

How close are we to hearing the full gravitational wave symphony?

If you are familiar with astronomy and electromagnetic radiation, you know that it takes different instruments to detect different wavelengths of light. So, for instance, as the James Webb Space Telescope (JWST) observes the cosmos in low-frequency longwave infrared light, NASA’s space-based Chandra X-ray Observatory examines celestial objects via energetic high-frequency, short wave light. 

Similarly, detecting the different gravitational waves requires using different instruments. Current operating gravitational wave detectors LIGO, Virgo, and KAGRA are laser interferometers with two sensitive laser arms that stretch for miles. The laser arms of LIGO, for example, stretch for four kilometers over the ground, and even under it, across the landscape at two locations in southeastern Washington State and rural Livingston, Louisiana.

The lasers are usually “in phase”, meaning when they come together, they amplify each other via a quantum phenomenon called “constructive interference”. If, however, gravitational waves pass over the arms, the stretching and squeezing of spacetime they cause results in the lasers being knocked out of phase, meaning then they meet the amplification is wiped out. When employed on Earth, this method can detect gravitational waves with frequencies from milliseconds to seconds and wavelengths in the region of thousands of miles from colliding neutrons, stars, and black holes.

The sensitivity of these interferometers on Earth is limited by interference or “noise” from Earth-based sources of vibration, and to overcome this, astronomers are currently planning to put a gravitational wave-detecting interferometer into space. 

The Laser Interferometer Space Antenna (LISA), currently being developed by NASA and European Space Agency (ESA), will consist of three spacecraft with laser arms stretching for around 1.6 million miles (2.5 million kilometers), forming an equilateral triangle. Free from Earth-based noise, LISA will be able to detect lower-frequency gravitational waves, also from compact binary systems, but from those that are closer together than the neutron star and black hole pairings heard by LIGO.

LISA isn’t won’t be capable of detecting lower-frequency gravitational waves from colliding supermassive black holes in the early Universe, which were detected this year by NANOGrav. The tool used in this case was pulsars, which because of their rapid rotation, can be used by a precise timing mechanism. 

Via three radio observatories, the Arecibo Observatory in Puerto Rico, the Green Bank Telescope in West Virginia, and the Very Large Array in New Mexico, NanoGrav turns 68 pulsars within the Milky Way into a huge gravitational wave antenna the size of the entire galaxy called a pulsar timing array. The squashing and squeezing of spacetime as gravitational waves wash over these sources cause tiny disruptions in these pulsars’ periodicity, which can be detected when a large sample of pulsars are considered together.

Even pulsar timing arrays aren’t capable of detecting the lowest frequency, longest wavelength gravitational waves, such as those of the Stochastic Background from the Universe’s earliest moments. It is, however, possible that these primordial gravitational waves could be detected by examining the cosmic microwave background, radiation that represents the first light that shone through the Universe and thus acts as a fossil record of the earliest points in cosmic history. 

To think of how extraordinary humanity “hearing” any of this symphony is consider this: the stretching and squeezing of spacetime they represent is tiny, about one part in a quadrillion (1,000,000,000,000,000). Einstein himself, though arguably the “father” of gravitational waves, never believed that humanity would have the tools needed to detect even the most energetic spacetime ripples. 

Fortunately, the great physicist was wrong, and by combining the detection of gravitational waves, humanity can both “see” the Universe in electromagnetic radiation and can “hear” it via these ripples in spacetime. 

This has given rise to an entirely new phase in astronomy called multi-messenger astronomy, a hybrid method of investigation which, though still in its infancy, promises to unlock the secrets of the Universe as never before. 

References:

What are Gravitational Waves?, LIGO Caltech, Accessed 01/08/23, https://www.ligo.caltech.edu/page/what-are-gw#:~:text=Though%20Einstein%20predicted%20the%20existence,20%20years%20after%20his%20death

Gravitational wave spectrum, Caltech, Accessed 01/08/23, http://www.tapir.caltech.edu/~teviet/Waves/gwave_spectrum.html

Low-Frequency Gravitational Waves, Nanograv, Accessed 01/08/23, https://nanograv.org/science/topics/low-frequency-gravitational-waves

The spectrum of gravitational waves, ESA, Accessed 01/08/23, https://www.esa.int/ESA_Multimedia/Images/2021/09/The_spectrum_of_gravitational_waves

Feature image credit: Artist’s interpretation of an array of pulsars being affected by gravitational ripples produced by a supermassive black hole binary in a distant galaxy. Credit: Aurore Simonnet for the NANOGrav Collaboration