Black Holes
Black holes may be heard but not seen. As the death state of a star, black holes emit no light. They are dark against the dark sky. But like mallets on a drum, black holes can ring out a song on space itself in the form of gravitational waves. Monumental Earth-based detectors such as LIGO and the planned space-based mission LISA aim to record the songs from space for the first time thereby turning up the volume on the soundtrack to the Universe.

There is no sound in empty space. But when the gravitational waves hit the Earth, detectors in the next few years will measure the stretching and shrinking of space and will be able to amplify the result as sound. To hear the sounds of two black holes ringing space, play the movies below.

In this video, two black holes of equal mass collide. Each is taken to have 10 times the mass of our sun. Starting from a distance of over 1,700 km apart, the black holes complete an average of 11 orbits per second around each other at an average speed of 0.4 times the speed of light, with the entire collision taking less than 90 seconds in real time. The resulting gravitational wave frequencies range from 7 Hz to 900 Hz. Since the two black holes have the same mass, they follow an almost identically circular path at extreme speed, making them appear in this simulation as having overlapping orbits. In reality, however, the two black holes are directly opposite each other in their orbital paths at any given time.

In this video, two black holes of different masses collide. The smaller (seen here in red) has a mass of 3 times the mass of our sun, while the larger (seen here in yellow) is 3 times more massive, with a mass of 15 times that of our sun. Starting from a distance of almost 4,000 km apart while each spinning in the plane of orbit, the black holes complete an average of 10 orbits per second around each other at an average speed of 0.8 times the speed of light, with the entire collision taking less than 1 minute 20 seconds in real time. The resulting gravitational wave frequencies range from approximately a few Hz to over 1200 Hz towards the end.

In this video, a neutron star collides with a black hole. The former (seen here in red) has a mass typical of a neutron star, or about 1.4 times the mass of our sun, while the latter (seen here in yellow) is 10 times more massive, or approximately 14 times the mass of our sun. In this case, both compact objects are spinning, which causes the entire plane to precess in space making the sound quieter when pointed away from us and louder when pointed toward us. Starting from a distance of over 3,400 km apart, the objects complete an average of 11 orbits per second around each other at an average speed of 0.8 times the speed of light, with the entire collision taking approximately 3 minutes 45 seconds in real time. The resulting gravitational wave frequencies range from 2 - 20 Hz, to 1040 Hz towards the end.

Finite Universe
Our universe appears to stretch nearly thirty billion light years across. As far as the eye can see, there is no visible bound to spacetime. Still the universe may not be infinite. There was once a cultural prejudice that the earth was flat and unconnected, so much so that explorers were feared to have fallen off the edge. The assumption that space must be infinite may represent a similar bias. A tenable possibility is that space itself is not only curved, as Einstein suggested, but that it is also finite. A finite universe, and indeed a finite universe with several extra dimensions, may be a prediction of a theory beyond Einstein’s – the long coveted Theory of Everything. Even as we struggle to understand the universe as drawn by a TOE, recent Astronomical observations may be on the cusp of resolving this age old question: Is the universe infinite?

Theories of Everything
A physical Theory of Everything is the greatest ambition consuming theoretical physics. Yet last century we were forced to concede that there will never be a mathematical theory of everything. Kurt Gödel, Alan Turing, and Gregory Chaitin proved that our knowledge of numbers themselves is fundamentally incomplete. Most numbers are random, a toss of the coin. There are true relations among the numbers about which we can only prove that we can never prove them.

Many times in the history of physics, theories have been shaped by such profound limits. Einstein proposed a fundamental limit in the speed of light and thereby discovered Relativity. Heisenberg invoked an uncertainty principle in measurements of quantum phenomena and thereby laid a cornerstone for Quantum Mechanics. Alongside these should be listed the profound incompleteness in our knowledge of numbers – there can never be a mathematical theory of everything. The proposal is to define the limits mathematical incompleteness might set on a physical theory of everything. Just as Relativity emerged from the limit of light’s speed and Quantum Theory emerged from the limits of measurement, deep insight into the universe and its origins could emerge by confronting the limit of mathematical incompleteness.