Yesterday astronaut Scott Kelly returned from nearly a year in free fall aboard the International Space Station to join his identical twin brother Mark back on Earth. Due to their different spacetime paths, I estimate that Scott aged about 9 ms less than his brother, and therefore travelled about 9 ms into the future, becoming one of Earth’s most accomplished time travelers.

As predicted by the theory of relativity, identical twins Mark and Scott Kelly aged differently during Scott’s year in space. Photo credit: Robert Markowitz / NASA.

The familiar Pythagorean line element dl² = dx² + dy² + dz² (and corresponding metric) describes the geometry of Euclidean space. The Lorentzian line element – dτ² = ds² = – dt² + dx² + dy² + dz² = – dt² + dl² (and corresponding semimetric) describes the flat spacetime of special relativity, where space is measured in light-years and time in years. The Einsteinian line element dτ² = g_μνdx^μdx^ν describes the curved spacetime of general relativity, with an implied sum over the indices. From third semester physics, in flat spacetime the proper time increment dτ = √(dt² – dl²) = dt√(1 – v²) = dt/γ, where the relativistic stretch γ ≥ 1 regulates the time dilation. More generally, the length Δτ = ∫ dτ of a spacetime worldline is the proper time or aging along it (which is most evident in the observer’s rest frame).

In the curved, approximately Kerr spacetime of the rotating Earth, clocks tick faster with increasing altitude but slower with increasing speed. In low Earth orbit aboard the ISS, the speed effect dominates the altitude effect, sending Scott Kelly about 10 ms – 1 ms = 9 ms into the future. Furthermore, in curved spacetime, multiple free fall or geodesic paths between the same two events can have different lengths or aging, which can desynchronize clocks or twins without proper (as opposed to coordinate) acceleration — and without paradox.

One of the first things I did as a grad student in 1982 was tour the Laser Interferometer Gravitational Wave Observatory (LIGO) prototype on the Caltech campus about a block from my dorm. It was housed in a utilitarian L-shaped building wrapped around the corner of another building. I toyed with the idea of working with Kip Thorne and Ron Drever on LIGO, perhaps making a career of it. I would be a small part of a large and long collaboration, but one that would probably make history. I chose a different path, but I never forgot LIGO, and I have closely followed its progress ever since. In 2007, I even co-advised Stephen Poprocki’s senior I.S. “Bayesian Source Direction Determination for Gravitational-Wave Bursts”, which was a small contribution to the LIGO effort.

A packed crowd of Wooster physicists eagerly awaits the news from LIGO.

Last Thursday morning, I was thrilled to sit with the Wooster physics department in a crowded Taylor 111 watching the LIGO team announce the first direct detection of gravitational waves. I got goosebumps reading the discovery paper in Physical Review Letters. However, during a later replay of the press conference, I heard Kip say Ron Drever was too ill to be there, but his family sent their best wishes. Sadly, the New York Times reports that Ron is in a nursing home in Scotland suffering from dementia, this historic discovery apparently too late for him to savor.

Audible chirps as proper distances between LIGO mirrors change by a few thousandths of a proton diameter in response to a binary black hole merger over a billion years ago.

Gravitational waves are the analogue for gravity of what light is for electromagnetism but about 10^{40} times weaker. Over a billion years ago, two black holes spiraled together, merged, and rung down, radiating away the equivalent of about 3 solar masses of energy in a third of a second with more power than the luminosity of the entire observable universe. Last September 14th, gravity waves from the merger passed through Earth, stretching and expanding the 4-km long arms of the two LIGO interferometers, which were thousands of miles and several milliseconds apart, by a few thousandths of a proton’s width. The resulting chirps in strain were visible to the eye above the noisy backgrounds. History had been made, and a new era in astronomy had begun.

The moment we first saw the now-famous plots of the gravitational wave signals.