Why nothing goes faster than light

Shine a torch at a wall three metres away. The light gets there about ten nanoseconds later, which is why nobody in the whole of human history noticed by eye that it took any time at all.

It does, and the figure is 299,792,458 metres per second. That isn't a measurement any more. Since 1983 the metre has been defined as the distance light covers in one 299,792,458th of a second, so the speed of light is exact by committee decision. Measure it more carefully today and you're refining the length of the metre, not the speed.

The number isn't the interesting bit. The interesting bit is that it's a ceiling, and that the ceiling has almost nothing to do with light.

Light was just the first thing caught doing it

Galileo tried the obvious experiment. Two men, two lanterns, two hilltops, uncover on a signal. He measured human reaction time and nothing else, and concluded that light was either instantaneous or extremely quick, which is a fair summary of a failed experiment.

The first real answer came out of bookkeeping about a moon. Ole Rømer, working at the Paris Observatory in 1676, was tracking the eclipses of Io, the innermost large moon of Jupiter. Io ducks behind Jupiter on a tight schedule, so it makes a decent clock. Rømer found the clock ran late when Earth was on the far side of its orbit from Jupiter, and early when Earth was close. Io wasn't misbehaving. The light simply had further to come. From the size of the drift he argued that light takes time to cross the Earth's orbit, which was an outrageous thing to say in 1676 and was also correct.

Fizeau brought it down to earth in 1849 with a spinning toothed wheel, a mirror on a hill about eight kilometres away, and a lot of patience. Spin the wheel fast enough and the returning flash comes back to find a tooth in the way instead of a gap. From the speed of the wheel you get the speed of the light. He was off by about five per cent, which for a first ground-based attempt is remarkable.

Then the theory arrived from an unexpected direction. In the 1860s James Clerk Maxwell tidied up electricity and magnetism into a single set of equations, and the equations coughed up a wave that travelled at a speed built entirely out of two constants measured in laboratories with batteries and coils. Nothing in that work was about light. The speed came out matching the measured speed of light anyway. Maxwell took the hint.

Why you can't push a heavy thing up to it

Here's the version people usually get told: as you go faster you get heavier, so it gets harder to accelerate. That's a serviceable picture but it puts the strangeness in the wrong place, because you never feel heavy. In your own frame you're always at rest, and nothing about you changes at all.

What actually happens is that energy and speed stop being tied together the way slow experience suggests. Double the speed of a bicycle and you quadruple its kinetic energy; that's the familiar rule, and it's an approximation that only works well below light speed. The real relationship involves a factor that runs to infinity as speed approaches c. At ten per cent of light speed the correction is half a per cent and you'd never notice it. At ninety per cent it's more than double. At 99.99 per cent your energy is seventy times what the schoolbook formula predicts.

Which means the last sliver of speed is where all the money goes. Pumping in more energy buys you more energy, more momentum, more punch on impact — but progressively less speed. You can spend forever and never arrive.

The Large Hadron Collider is the practical demonstration. Its protons carry thousands of times their own rest energy and travel at something like 99.999999 per cent of c, which sounds like a rounding error away from the limit. In absolute terms they're trailing light by roughly three metres per second. Every upgrade in the machine's history, every extra magnet and every added gigaelectronvolt, has been spent shaving fractions off that gap. It won't ever close.

Speeds don't add the way you'd expect

The naive objection is easy to state. Fire a rocket forwards at three-quarters of light speed from a ship already doing three-quarters of light speed, and surely you've got one and a half times c.

You haven't. Velocities don't simply add; they combine through a formula that has the sum sitting on top of a correction term. Run the numbers and 0.75c plus 0.75c comes out at about 0.96c. Try it with two speeds of 0.99c and you get 0.99995c. Feed the formula anything at all below c and it hands back something below c. Feed it c itself and it hands back c, from any starting speed, which is the whole strangeness of relativity in one line of arithmetic.

At everyday speeds the correction term is so close to zero that ordinary addition works perfectly, which is why nobody spotted any of this until people started looking at light.

It's the speed of causality, and light just happens to hit it

Calling c the speed of light is a historical accident. A better name is the speed of causality — the maximum rate at which any influence, of any kind, can get from one place to another.

Massless things travel at exactly c, and have no choice in the matter. Photons are massless, so light does it. Gluons do it. Gravity does it too: when the merger of two neutron stars was detected in August 2017, the gravitational waves and the gamma rays arrived about 1.7 seconds apart after a journey of roughly 130 million light-years. That's an agreement to about one part in a thousand million million, and it settled a long argument about whether gravity propagates at c. It does.

Neutrinos, which do have a small mass, come in just underneath. They can't quite manage it either.

The reason the limit is about causality rather than about light comes from relativity of simultaneity. Observers moving relative to one another don't agree on which distant events happened at the same moment, and that disagreement is not an illusion or a measurement error — it's how the geometry works. Grant that, and allow any signal to travel faster than c, and you can construct a chain of observers in which the signal arrives before it was sent. Not "arrives suspiciously quickly". Arrives earlier. You could answer a question you haven't been asked, or arrange for a message to prevent its own transmission.

So the speed limit isn't a stubborn engineering problem. Dropping it means dropping cause and effect, and physicists would rather keep those.

The things that do outrun light, and why nobody minds

Plenty of things beat light. None of them carry information, and that's the entire distinction.

Start with the easy one. In water, light propagates at about three-quarters of its vacuum speed, because it keeps interacting with the medium on the way through. A fast enough charged particle from a reactor or a cosmic ray can beat that local speed, and when it does it drags a shockwave of light behind it — the reason the water in a reactor pool glows blue. That's Cherenkov radiation, discovered in the 1930s, and it's a genuine sonic-boom-for-light. No law is broken, because the limit that matters is c in vacuum and nothing here is close to it.

Then there's the searchlight. Sweep a powerful beam across the face of the Moon and the bright spot crosses the surface far faster than light could travel between the two points it touches. Nothing has moved along the Moon, though. Each photon travelled outward from the lamp at c and landed. The spot is a sequence of separate arrivals, not an object, and you couldn't use it to get a message from one lunar crater to another.

Wave physics offers a subtler version. Inside certain media and waveguides the phase velocity of a wave — the speed of the pattern's crests — genuinely exceeds c, and under odd conditions so does the group velocity. What can't be pushed past c is the front, the first faint disturbance that says anything has arrived at all. Information rides the front.

The largest example is the universe itself. Space between distant galaxies is expanding, and expansion isn't motion through space, so no local speed limit applies to it. Far enough away, the recession rate exceeds c, and the galaxies out there aren't racing anywhere — the distance between us is simply growing. This is also why the observable universe is about 46 billion light-years in radius despite being only about 13.8 billion years old. The light took 13.8 billion years to reach us; its source has been carried much further out in the meantime.

Quantum entanglement gets dragged into this constantly and doesn't belong. Measuring one half of an entangled pair does instantly fix the statistics for the other half, but the outcome you get is random, and the person at the other end sees random results too. They can't tell whether you've measured yet. Comparing notes and finding the correlations requires a phone call, and the phone call runs at c like everything else. The formal statement of that is the no-communication theorem, and it has held up perfectly.

What the limit does to clocks

A universal speed limit forces time itself to be flexible, and the effect is measured routinely.

Muons make the cleanest demonstration. They're produced when cosmic rays hit the upper atmosphere, around fifteen kilometres up, and they decay with an average lifetime of about 2.2 microseconds. Even flat out at light speed that's roughly 660 metres of travel before most of them should be gone. They reach the ground in large numbers anyway. Rossi and Hall showed this in 1941 by comparing muon counts on a mountain and at sea level. From our point of view the muon's internal clock is running slow. From the muon's point of view the atmosphere is squashed thin. Both descriptions give the same answer, which is generally how relativity behaves when you push at it.

In 1971 Hafele and Keating put caesium clocks on scheduled airliners, flew them east and west around the world, and compared them with clocks left at the US Naval Observatory. The travelling clocks disagreed with the stay-at-home ones by tens of nanoseconds, in the directions predicted, with speed and altitude pulling opposite ways.

Satellite navigation is the version in your pocket. The clocks aboard GPS satellites lose about 7 microseconds a day to their orbital speed and gain about 45 to weaker gravity, a net gain of roughly 38 microseconds daily. Left uncorrected that's a positioning error growing by about ten kilometres a day. The system builds the correction in. Relativity isn't an exotic effect at the edge of the universe; it's a line item in a receiver's firmware.

What the limit does to distance

The other consequence is that the universe is enormous and the post is slow.

A light-year is about 9.46 trillion kilometres. Proxima Centauri, the nearest star, sits at 4.2 of them. Voyager 1, the fastest thing we've ever thrown out of the solar system, manages around 17 kilometres a second, and at that rate a four-light-year crossing takes something like 75,000 years. There's no trick of engineering hiding behind that figure. The energy needed to push serious mass to a serious fraction of c is the problem, and the closer to c you aim, the worse the bill gets.

Closer to home the limit shows up as lag. The Moon is 1.3 seconds away, which is why the Apollo transcripts have that stilted rhythm. Mars ranges from about 3 to about 22 minutes one way depending on where the two planets are. You can't drive a rover on Mars with a joystick — by the time you see the rock, the rover has either hit it or not. That's why the machines are built to make their own decisions about where to put their wheels.

And it means the sky is a history archive. Every telescope is a time machine pointed the wrong way round.

The one time somebody thought they'd broken it

In September 2011 the OPERA collaboration announced that neutrinos sent from CERN to a detector under the Gran Sasso mountain in Italy, 730 kilometres away, had arrived about 60 nanoseconds early. Faster than light, by a whisker.

What happened next was the field working properly. The team didn't claim a discovery; they published the anomaly and asked openly for someone to find their mistake. Physicists generally assumed there was one, partly because neutrinos from supernova 1987A had arrived on schedule after 168,000 years, which leaves very little room for them to be quick.

The mistake turned up in the plumbing. A fibre-optic connector carrying the timing signal wasn't seated properly, and a clock oscillator was running slightly off. Correct both and the neutrinos land on time. The result was withdrawn in 2012 and the collaboration's leadership resigned.

It's a good story to keep, because it's the closest anyone has come, and it was a loose cable.

What's actually still open

Relativity forbids accelerating through the light barrier. It doesn't, strictly speaking, forbid geometry that connects distant places by a shorter route, and there's a small serious literature on that. Miguel Alcubierre wrote down a spacetime in 1994 in which a bubble of flat space is carried along by contracting space in front of it and expanding it behind, with nothing inside the bubble ever exceeding c locally.

Be clear about the status of this. It's a solution to Einstein's equations written backwards — pick the geometry you want, then read off the matter distribution required to produce it. The answer comes back demanding large amounts of negative energy density, which no known substance provides in useful quantities. It's a piece of mathematics, not a project, and treating it as a prototype is how good physics becomes bad television.

The honest position is that the ceiling has been probed for over a century by increasingly nasty experiments and hasn't shifted. Particle accelerators, atomic clocks on aeroplanes, neutrinos from exploding stars, gravitational waves from colliding neutron stars — all of it lands on the same number.

Which leaves one last way to look at it, and it's the one that makes the limit feel less like a fence. Everything moves through spacetime at c, always. Sitting still, all of that motion is directed through time. Start moving through space and some of it gets diverted sideways, and your progress through time slows to compensate. You're not being held back from the speed of light. You've been travelling at it the entire time, in the only direction you normally notice.