Time travel

Toss a ball straight up in the air while walking, and it will fall back into your hand just as it would when standing. The ball has only up and down motion for you. For a stationary onlooker, however, your ball tracks more quickly through a longer parabolic arc, with up, down and forward motion. The frame of reference thus determines the dynamics of motion. Galileo perfectly understood this basic principle of relativity1; Newtonian physics entirely accommodates it2.

If you travel fast enough and for long enough, on a long-haul flight for example, then you might detect different physics, due to special relativity3. Bring along an atomic clock on an eastward flight around the world, outpacing Earth’s own eastward rotation, and you will find at journey’s end that time itself has passed detectably more slowly for you than for those you left behind, and yet more slowly than for those flown westwards4. Although you won’t feel it, you will have aged fractions of a microsecond less than them.

Board a rocket to space, and you might detect another effect, due to general relativity5. As the rocket lifts up and away from Earth’s gravitational pull, your onboard atomic clock will tick detectably faster with each centimetre of altitude6. Satellite communications and GPS only work by accounting for dependencies of time itself on the frame of reference7.

Suppose that you wish for your space odyssey to carry you ever faster from Earth8. As your relative speed increases, so also does your relativistic mass3, ever raising the energy requirement to go faster. You approach only asymptotically towards the speed of light, meaning that you never quite attain its 299,792 kilometres per second in the vacuum of space9. Special relativity reserves this ‘universal’ speed – constant across all frames of reference10 – for the photon, the massless quantum of all electromagnetic radiation11,12. You can always radio home to Mother Earth, then. But beware the greater passage of time back there, for you will be reaching years into your future13.

Galileo Galilei’s understanding of basic relativity, 1632.

Isaac Newton’s classical mechanics, 1687.

At the age of 16, Albert Einstein wondered what it would be like to run after a wave of light at the speed of light. He was tempted to think the wave would appear frozen in front of him. But that notion was incompatible with experiments published a few years earlier. In 1887, Albert Michelson and Edward Morley had demonstrated that light always has the same speed for whoever is measuring it, regardless of their motion. Einstein faced an apparent contradiction, which 10 years later would bring him to a radical solution: the universal speed of light meant that time itself must vary between observers in relative motion. Time was not absolute.

Let’s suppose that Einstein is falling behind just a little in his pursuit of the light wave. He shines his torch in front of him – does the light from his torch catch up with the light wave ahead? No, it can’t travel faster than the universal speed of light. The light wave he’s chasing and the light wave sent out from his torch both travel at the same speed. This can be true for Einstein’s own measurements only if something else changes: his pocket-watch would run more slowly and distance would shorten along his direction of motion, compared to the measurements of observers moving relative to him. In such cases of steady relative motion, each observer finds that the other’s clock runs more slowly. (This happens without contradiction because the observer’s frame of reference dictates what counts as the same time when comparing distant clocks). As much as time stretches, distance must shrink in compensation to preserve light’s universal speed, measured as distance over time. Space and time thus form a single structure: spacetime.

Einstein published his resolution as the special theory of relativity in 1905, introducing the ideas of time-dilation and length-contraction for moving objects, relative to any observer.

In 1972, Joseph Hafele and Richard Keating flew four atomic clocks around the world on commercial airliners, once eastward and once westward. On their eastward round-trip – in the direction of Earth’s rotation, the clocks lost a few hundredths of a microsecond compared to a ground-based reference clock. On the westward trip – against Earth’s rotation, they gained on the reference by a few tenths of a microsecond.

These findings accorded with predictions of special and general relativity for asymmetrical movements that brought the travelling clocks back to the same starting point. For speeds of motion as they would be perceived by an inertial observer looking down on the North Pole from a great distance, the fastest-moving (eastbound) clocks ticked some 60 nanoseconds more slowly than the reference clock, which ticked some 270 nanoseconds more slowly than the slowest-moving (westbound) clocks. Thus did time dilate in accordance with special relativity. Compared to the reference, time gained by the westbound clocks greatly exceeded time lost by the eastbound clocks because the high altitude of their flights weakened the effect of time dilation due to Earth’s gravitational pull. This prediction of general relativity was expressed as an additive effect for the westbound clocks and a cancelling effect for the eastbound clocks.

The tiny overall time differences between all the atomic clocks illustrate the almost negligible effects of special and general relativity at these scales, allowing us to perceive time as effectively absolute in everyday experience.

Albert Einstein’s theory of general relativity, 1915.

Optical lattice clocks, invented in 2015, have an accuracy of 1 second in 40 billion years; they tick detectably faster with each centimetre of altitude.

GPS was first developed in 1973 by the US Department of Defense to enhance the positioning capability of its military forces.

Only slightly more wishful than the Starshot lightsail, 2018.

The Danish astronomer Ole Rømer achieved the first quantification of the speed of light, in 1676, by timing the eclipses of Jupiter’s moon Io, as it orbited behind Jupiter every 42.5 hours. He noticed that the eclipses appeared some minutes later when Jupiter was furthest from Earth, and earlier when it was closest to Earth. This discrepancy led him to estimate the time taken by light to cross Earth’s orbit, at 22 minutes. He thereby provided the first observational proof that light is not instantaneous, as Galileo had suspected, but has measurable speed.

Rømer was considering the speed of light as it passes through the vacuum of space. Light is slowed by passage through substances, including air – taking 90 km/s off its speed, water – reducing its speed by one-quarter, and glass – reducing its speed by one-third. This slowing is caused by interference with electromagnetic waves of jiggled electrons, and full speed is restored instantly upon return to a vacuum. The pace changes caused by substances have the effect of refracting the light, for example making a straight stick appear bent at its point of entry into water.

Michelson-Morley experiment, 1887.

James Maxwell’s theory of light as electromagnetic radiation, 1865.

Albert Einstein’s photon hypothesis, 1905.

For every hour you experience on a spacecraft travelling at 25% the speed of light, about 1 hour and 2 minutes will pass on Earth. Your hour will correspond to about 2 hours on Earth when your speed achieves 87% of light speed, and about 7 Earth hours at 99% of light speed.