Hey guys, nice to see you 😉
As you are propably aware of, this week all of the winners of the prestigious Nobel Prize are beeing announced.
And with respect to physics the honor goes to Rainer Weiss, Kip Thorne and Barry Barish for the detection of "Gravitational Waves" - a prediction of Albert Einstein's theory of relativity in 1916 and subject of speculation before under Heaviside and Poincaré.
But what is a gravitational wave? I would like to provide a short explanation from the perspective of cosmology:
What are we studying anyway?
To comprehend a gravitational wave one must first understand the physical foundation of our cosmos. To our current knowledge, the laws of nature governing our universe and the behaviour of spacetime are most accurately characterized by Einstein's Theory of General Relativity.
It is the theory which accurately explains various celestial phenomena both qualitatively and quantitatively such as:
- Bending of light trajectories by black holes and massive objects ("Gravity lensing")
- Time dilation in the gravitational field
- Perihelion precession (elliptical orbits e.g. of planets are not static but rotate themselves)
- Gravitational redshift
- etc.
Gravitational Lensing of colliding black holes, LIGO, Simulating eXtreme Spacetimes under CC BY-SA 4.0
The main essence of general relativity observation that we do not live in a 3-dimensional space that evolves with time, but rather in a 4-dimensional spacetime in which time is just one additional (albeit discerned and special) dimension of our world.
This spacetime is mathematically described in term of a peudo-Riemannian manifold whose points correspond to events in space and time. So basically the event of you in your kitchen turning on the coffeemaker this morning is a point of this manifold we could assign spatial and temporal coordinates to.
Similarly our notion of distance between events in this world now incorporates both space and time and is (locally) measured by the so-called metric or fundamental tensor (gμν) which in any given point may be represented by a 4×4 matrix.
Essentially (gμν) together with its first and second derivatives describes the local structure of spacetime in any point, including its Ricci curvature (Rμν).
Conversely, the metric tensor is implicitly determined (up to coordinate transformation) by the so-called mass energy tensor (Tμν) which is kind of a density function characterizing the distribution of mass and energy in the universe.
Specifically the functional dependence between these quantities is given by the famous Einstein equations
Rμν - Λgμν = (8πG/c4)(Tμν-(1/2)Tgμν)
(Where Λ is the cosmological constant, G the gravitational constant, c the speed of light and T the trace of Tμν)
Gravitational Waves
Certain celestial movements may locally disturb the mass energy tensor in a time dependent way, e.g. massive objects such as black holes or neutron stars orbiting each other. By the above Einstein equations, this will also create a small perturbation of our metric tensor g that will start propagating though space - a gravitational wave is born.
By a general theorem from general relativity - Birkhoff's theorem - this can only occur when the mass distribution of the system in question is not spherically symmetric. So a pulsating star or an exploding supernova will in general not generate gravitational waves unless they are for some reason not symmetric.
Representation of waves generates by 2 neutron stars orbiting each other, Wikipedia
Gravitational Waves produced by colliding black holes, Simulating eXtreme Spacetimes under CC BY-SA 4.0
Gravitational waves in this context can be considered as ripples in spacetime spreading from their point of origin. These waves propagate through the largely empty universe at the speed of light until they eventually reach the earth - where they alter our spacetime just by a tiny amount.
Depending on the polarization of the gravitational wave they stretch space in some direction and quench it in another. Below you see an exaggerated illustration of a wave on the relative distances of "ring of cosmic dust in a vacuum" in a plane orthogonal to the wave vector:
"Plus" polarization, Wikipedia
"Cross" polarization, Wikipedia
How do you detect gravitational waves?
This time dependent fluctuation may then be picked up by terrestrial interferometers.
An interferometer consists of two orthogonal long vacuum tubes in in which one coherent laser beam is split up into two half in-phase half-beams by a half-mirror. Each beam travels the length of the tube and is reflected by a mirror at the end. Using another mirror, both beams are then made to converge onto a single optical sensor. This will create an interference pattern of both half-beams that depends on the relative distance both beams travelled (similar to a double slit Laser experiment for instance).
Laser interferometer schematic, Wikipedia
This allows to detect differences (or time dependent fluctuations thereof) in the interferometers "arm length" in order of magnitude of the laser's wavelength, so typically a couple of 100 nanometers. Assuming the overall interferometer dimensions are sufficiently large (state-of-the-art observatories such as the LIGO in the USA or the GEO in Germany have 4km and 600m respectively) this enables astronomers to pick up on really tiny disturbances of the metric tensor by gravitational waves.
In fact those two observartories in addition to several hundred up to thousands of scientists working for or collaborating with them are the major elements to have made the discovery of gravitational waves possible. So I would like to congratulate all of them to their good work and this accomplishment.
This is in essence a brief overview of the topic of gravitational waves and how to to prove their physical existence.
Hopefully this has been enlightening to you and have a nice evening!
References:
- Viatcheslav Mukhanov, Physical Foundations of Cosmology , Cambridge university press
- https://en.wikipedia.org/wiki/Gravitational_wave
- https://www.black-holes.org/
- https://en.wikipedia.org/wiki/Einstein_field_equations