On Gravitational Waves

With LIGO (pioneered by the greats like Rainer Weiss, Kip Thorne, and Ronald W. P. Drever) going nuts in September 2015, and twice later, gravitational waves seem to be physical reality, not just predictions. They are significant not only because they are another confirmation of Einstein’s Theory of Gravity, but also because they are key to a new and promising method of observing the universe. They were predicted out of the fundamental field equations of gravity that were established by Einstein. Given that all my articles seem to be centered around Einstein, it seems that I am a fanboy. I do not deny that I am one, but the fact remains that a lot of developments in physics in the 20th century happened due to that man. He laid the foundations of relativity and formulated a theory of gravity that explained everything that Newton could not and more, as well as was responsible for the development of Quantum Mechanics. So really, being a fanboy is not abnormal. But I digress.

Gravitational waves are the best example (after Quantum Mechanics) of how nature is fundamentally “nutty” and “fuzzy”. The fundamental counterintuitiveness of these aspects of physics is what brings abstractness into a concrete attempt at understanding nature. The Field Equations of Gravity, as given by Einstein, tell us how spacetime and matter interact. Spacetime is the mathematical structure that underlies the relativistic description of nature. The motion of all bodies in nature is encapsulated in this fabric.

Thinking of spacetime as having three dimensions of space and one of time is not completely accurate. It is just the most accurate way that we can represent it. In reality, it is just a big mashed-up mess. We cannot describe directions without space and we use these directions themselves to describe space. We are stuck in this kind of a loop using two interdependent quantities to describe each other. However, thinking of this fabric as a rubber sheet and creating analogs is just fine. It helps make visualizations easier and develop intuition.

In the previous article, I mentioned about metrics and other aspects of the Field Equations. Metrics describe the structure of the surface of spacetime. It is basically a function that helps us define distances on a given surface. The Field Equations tell us (as so aptly stated by John Wheeler) that “spacetime tells matter how to move and matter tells spacetime how to curve”. The existence of matter causes spacetime to curve. This curvature tells matter how to move. It is this curvature that causes planets to be in the orbits that they are in. It is this curvature that tells light how to bend around heavy objects.

An interesting side note, Newton’s equations tell us that gravity can only be felt between particles with masses. So, particles that do not have any rest mass have should not ideally be affected by gravity. But we observe that light is actually curved by Stars and other bodies with high gravitational effects. Einstein’s theory tells us that light curves, not because it is affected by gravity, but because the path of light is affected by gravity. Since the path itself is curved, light too must follow a curved path. This is analogous to taking a rubber sheet and drawing a straight line on it. Consider this line to be the path of light. Now, if there is an object with significant gravity in its path, we know from the field equations that it will curve spacetime. So, in our analogy, we press down on the rubber sheet (to simulate gravity) and we can see that the straight line itself is curved. Basically, light always travels in a straight line. It always takes the shortest path between two objects, once we consider all the constraints.

Now, going back to the topic, Gravitational Waves. Gravitational Waves are, as the name suggests, are waves in spacetime itself. For such waves to be formed, an intense amount of energy has to be injected into spacetime. When enough energy is injected into this fabric, the very fabric itself starts to oscillate. Waves are generated. These waves are called gravitational waves.

The first gravitational wave was suggested by Joseph Taylor Jr. and Russell Hulse. They observed a binary system of a pulsar in an orbit around a neutron star. They observed that the orbital radius of the orbiting pulsar was reducing. This would mean the loss of energy. No energy burst was observed from the binary system, so where was this energy going? Turns out, this energy was being injected into the fabric of spacetime. It was causing space-time itself to oscillate. It can also be caused due to a binary system of Black Holes. As the Black Holes rotate around each other, their speeds go close to the speed of light. They affect the neighboring spacetime to a great extent.

Think of it like dropping a stone into a pond. You can observe ripples. Now, instead of the stone, imagine two of them rotating around each other at unimaginably fast speeds. This would generate incredibly big ripples in the pond. That is exactly what happens. The pond is like spacetime, and the stones are like the two Black Holes.

For Black Holes, it goes one step further. Gravitational Waves are generated due to their mutual rotation, but when Black Holes merge, their final mass is less than the mass of the sum of the masses of the merging Black Holes. Where does this mass go? Turns out, according to mass energy equivalence, this mass gets converted into energy and injected into spacetime. This would be seen as a final burst of gravitational waves.

Interestingly, I had a few friends who had asked me that if we consider wave-particle duality, then why do gravitational waves not imply the existence of a particle for gravity, the graviton? The answer is that gravitational waves do not correspond to any particles. This is because gravitational waves do not exist by themselves, they exist as an effect of certain phenomena. All the fundamental particles can exist as waves by themselves, they do not require any other phenomena to create it. Also, another reason why this fails is that wave particle duality is seen quantum mechanically, Gravitational Waves are classical. General Relativity, is the most accurate description of the classical world that we have till date. So, this association will not work.

The intense interest of observing gravitational waves is not because it is another confirmation of General Relativity, but because of its immense applications in astronomy and cosmology. This opens a new field of observational cosmology or astronomy called gravitational wave astronomy. It will improve our ability to observe warped space-time and definitely improve our chances of observing and understanding Black Holes.