The speed limit

We keep pumping energy into , a thousandfold, a millionfold, a trillionfold its energy at rest. The speed shoots up at first and then creeps: every extra nine after the decimal point costs √10, about 3.2 times, the energy. The energy goes into the momentum, which has no ceiling; the speed has one. The clock on the train is the same γ seen from the other side: the faster it goes, the slower its time runs, and at c it would stop. The protons in the Large Hadron Collider, at 6.8 TeV, go at 0.999 999 990 c. The most energetic particle ever seen, the "Oh-My-God particle" caught over Utah in 1991, a proton with 3.2 × 10²⁰ eV, was still slower than light, by about four parts in 10²⁴.

Light has no rest mass, so it never accelerates and never slows down: it exists only at c. The same goes for gravitational waves. On 17 August 2017 detectors caught the waves of two neutron stars colliding 130 million light years away, and 1.7 seconds later a burst of gamma rays from the same event: after 130 million years on the way, a dead heat, which pins the speed of gravity to the speed of light within about one part in 10¹⁵. The chirp has its own room.

Neutrinos were long thought massless too. Then they turned out to change type on the way, from one flavour to another, which they can only do if they have mass (the Nobel prize of 2015), so they must go slower than light, if only just: the KATRIN experiment puts the mass below 0.45 eV. When supernova 1987A exploded 168,000 light years away, two dozen of its neutrinos were caught in Japan, the United States and Russia, hours before the light, but only because the light needed hours to get out of the dying star. Out in space the neutrinos fell behind by a few milliseconds at most, which is what the race shows with the mass at its upper limit.

The dots are galaxies, each standing still where it is, with the space between them growing. Pick a galaxy and it sends a flash of light towards us, now. Beyond about (the red line) space between us grows faster than light could cross it, so the galaxy moves away faster than light and, at first, so does its flash, although it is flying straight at us. Nothing is wrong: light is never overtaken locally, wherever it is; it is the road that is getting longer. Because the growth rate itself slows a little, a flash from just beyond the red line still makes it in the end. From beyond (the brass line), the cosmic event horizon, it never will: the dark energy makes the expansion speed up, and those galaxies have already said their last goodbye. Light from them that set off long ago is still arriving, and it arrives reddened, stretched by the same growth.

That is also how a universe old can have an observable edge away: the light from there has travelled for most of that time, and the space it crossed has kept growing behind it. The galaxies we see at a redshift above about 1.5 are moving away from us faster than light today.