Looking at the Universe through gravity

Here we go with another recent excitement in physics with an exceptionally high impact factor. This time, I will be talking about a discovery, not a tentative observation as in my previous post that can easily turn out to be a statistical fluctuation.

The news is that gravitational waves have been detected for the second time. But since I had not started blogging back in February 2016 when gravitational waves were detected for the first time, I will take you back to the first discovery before talking about the evolution of gravitational wave detectors into observatories.

First, let’s talk about gravitational waves themselves. These are traveling excitations of the spacetime (the four-dimensional fabric in which all physical particles live and interact) predicted by the general theory of relativity. For example, if such a disturbance were to pass through your body, you would be stretched in the transverse plane. The interesting fact about gravity is that the Einstein Field Equations, which describe the spatial and temporal evolution of the underlying gravitational field, admit a tensor source term. This means that the quanta that describe the interaction are spin-2 particles. This has the further implication that gravitational waves can only be produced if the second time derivative of the gravitational quadrupole moment is nonzero. As a result, gravitational waves are only produced by rotating and spherically asymmetric compact objects.

There is a caveat in this argument, though. In my previous post, I mentioned that gravitational coupling is very small compared to the other forces. In fact, it is so weak that typical gravitational waves produced by the acceleration of a planet-sized object (or anything smaller for that matter) are too weak to be picked up among the numerous sources of terrestrial noise. It takes episodes of extreme acceleration such as binary black hole inspirals or core collapse supernovae to disturb the spacetime strong enough so as to be detected far away. This statement depends on how massive and distant the merging objects are. The more massive or closer they are, the larger the volume in which the generated perturbations will possibly be picked up by potentially listening observers. And since gravitational field flux is proportional to the inverse square of the distance to the observer, receivers further away from the merger will pick up a proportionally weaker signal.

On 14 September 2015, we received such a signal. Each of the two detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) measured a relative change in the lengths of its two arms. Here, we are not talking about a change with arbitrary time evolution, though. In fact, the detector is subject to many sources of errors, e.g., digital, seismic, such that it continuously measures noise across a large bandwith. However the expected signal from a merger is an oscillation with an increasing frequency and amplitude, which then abruptly dies away. This waveform corresponds to the increase in the orbital frequency and acceleration of the merging black holes. As the black holes merge the gravitational excitations maximize and, then, vanish as the merged black hole settles to a stable state.

Below I included the time series detected by LIGO (top) and the modeled waveform (middle) along with the residual (bottom). The left pane shows the results from the interferometer in Hanford, Washington whereas the right pane shows data from detector in Livingston, Louisiana. The vertical axes show the strain, which is a dimensionless quantity giving the ratio between the observed perturbation and the baseline. Given a baseline of \(\sim\) 3 km, a strain measurement of order \(10^{-21}\) means that we are talking about a thousandth of the proton radius!

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Looking at the plots, the first striking resulting is the observation of the expected waveform which is also known as a chirp for good reasons. Next, the waveforms measured by the detectors agree up to a phase shift. One reason for the shift is that the two detectors are physically apart. Therefore the approaching wavefront hits the detectors at different times. By modeling the time difference, one can even localize the source to a disc on the sky. The second reason is that the detectors are misaligned (on purpose) so that the same wavefront is observed with a certain phase shift.

I think it is important to emphasize a fundamental point about the agreement. The fact that the two detectors agree up to a phase shift is not just a bonus that makes the measurement more credible. Quite the contrary, if you look for a certain waveform in a large enough dataset from a single detector, you will eventually find it. This is because the infinite monkey theorem guarantees that very unlikely waveforms will be observed if large enough samples are taken from a probability distribution of waveforms. The way to tell that a given observation corresponds to a measured signal and not to a statistical fluctuation of the background, is to make sure that the same waveform is observed in independent experiments so that low probabilities get multiplied.

The implication of this discovery is very profound. It is likely that full exploitation of gravitational wave observatories will wait for a few decades, as we learn to use gravitational waves to look at the Universe in ways that were inaccessible to us before. For instance, having multiple observatories will help us localize sources more precisely and detect many more (and fainter) mergers so as to make a population model of binary black hole mergers. There are also efforts to achieve longer baselines by sending laser interferometer probes into space. However this is a few decades into the future.

One goal that has already been achieved is the closure of a long chapter in the quest for understanding gravity. We now have direct observational evidence for all predictions of Einstein’s general theory of relativity. Nevertheless, we also have many other surviving pieces of evidence, which show that it must be wrong at small (quantum) or, possibly, very large (cosmological) scales. As we exploit gravitational excitations to understand the Universe, we will surely keep an eye on further precision tests of the general theory of relativity!

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