If I travel to Alpha Centauri at the speed of light, then look back at Earth… will I see the past?
BIG THE QUETION
SHORT ANSWER:
Actually you’d see what YOU think is the present, but the Alpha Centaurians will think it’s the past. Uh… it’s complicated…
LONG ANSWER:
So you’ve invented a magical space drive that lets your ship travel at light speed. Now you’ve done it.
As Einstein's fans know, nothing in the universe can move faster than light. Photons and various other massless particles can move at light speed – which is 299,792,458 metres per second in vacuum – but nothing made of matter can go faster.
That “massless” part is important, because travelling at 100% of light speed, at least with our current technology and understanding of physics, is also impossible.
See, the faster you want to go, the more energy you need to use to accelerate. And at the point where you want to accelerate from 99.999% the speed of light to full light speed, your ship's engine will need an
infinite amount of energy.
BUT MAGIC SPACESHIP?
Okay, so let’s leave that small technical detail aside, and pretend we’ve figured out how to accelerate a ship to light speed. Let’s also assume that our magic Space Drive lets us leave Earth, then immediately accelerate to light speed whenever we want..
In real life, a ship would need a period of time to accelerate, because jumping from zero to 1.079 million km/h in an instant would turn all the passengers into a sort of strawberry jam mush on the rear bulkheads. A real starship might even take years to accelerate up to a significant percentage of light speed – but more on that later. Let’s stick with the magic Space Drive for now!
It means we don’t need to add in a bunch of days or months or whatever for acceleration – or deceleration at the other end of the journey. It’s just: Press go, lightspeed, travel, press stop, arrive. Okay!
As you may have heard, the Alpha Centauri system is about 4.37 light-years from Earth. That’s the distance light will travel, through a vacuum, in four years, 135 days, one hour and 12 minutes.
And so this means, at light speed, it will take our ship exactly four years, 135 days, one hour and 12 minutes to make the journey to our nearest stellar neighbour.
(Actually, even 4.37 is an approximation. We’re getting better at measuring the distance to closer stars, but we’re pretty sure now that the system isn’t further away than 4.37 light-years…)
When you look up at Alpha Centauri, which is the brighter of the two Pointers near the Southern Cross, you’re actually seeing what the triple-star-system looked like four years ago. Well, four years, 135 days and the rest of it…
The point here to remember is this: it takes light itself four years (and a bit) to travel from Alpha Centauri to us, and the same amount of time for our Sun’s light to travel to Alpha Centauri. Four years.
GET ON WITH IT!
So to the question (at last): if we jump in our magic space drive ship, and zip over to Alpha Centauri, and then turn our ship’s telescope onto the Solar System, and look at Earth (it’s a really good telescope, okay?), how “old” will the Earth look?
For Alpha Centaurians, or indeed anyone who was already at Alpha Centauri before we arrived, the answer to this is simple. Let’s say we left Earth in late 2017, and arrived at Alpha Centauri in early 2022. To the people already there, the Earth will look as it did in 2017.
Because you can’t go faster than light, no matter how far you travel, anywhere in the universe, other stars and planets will always look as old as their distance in lightyears. If you can get your head around that, the whole business of cosmology will become approximately 9% less confusing.
Speaking of confusion: you might think that, if you travel for four years at light speed, then turn around and look at the Earth, the Earth will look four years older than the actual year. After all, everyone on the spaceport you’ve arrived at will agree with this. At Alpha Centauri, the year will be 2022, and the Earth will look like it did in late 2017.
Unfortunately, it’s more complicated than that. For YOU, anyway. Because of a thing called “time dilation”.
TIME DID WHAT NOW?
When you travel at so- called “relativistic” speeds – when the numbers get so big it's easier to measure in fractions of light speed
this make-believe colony at Alpha Centauri track your ship taking four years to make the crossing… for you the journey will seem to take no time at all.
That’s right. For a starship’s crew, travelling at 100% the speed of light feels just like using warp-drive.
To explain: Let’s say you plan to set off at midnight on 31 October 2017 (Halloween seems a fitting occasion for this craziness…).
You will settle back in your jumpseat, press the big red LIGHT SPEED NOW button, the magic space-drive will spool up… and then it will spool right down again and a window will pop up on your display saying “Destination reached.”
Inside the ship, your ship’s clock will read “2017, October, 31 – 00:00:01”, and the seconds will continue to tick away as normal. But outside, at the spaceport or whatever at Alpha Centauri, it’s 16 March 2022, at 01:12 in the morning.
Congratulations! As well as travelling over 30,700,000,000,000 kilometres in zero time, you’ve also somehow also travelled four years into the future… well, not the future, your future. Everyone else went the long way. Wait, what?. Your trip was instantaneous, and it took four years? At the same time? We told you it was complicated. Anyway, what this means in the real world, is that when you turn around and look at the Earth through your telescope, to you the Earth won’t look out of date, it will look like it did at the exact moment after you left. That’s because, by travelling at light speed, you were at the head of a stream of photons coming from the Solar System. No light could “beat” you to Alpha Centauri, but neither could you beat any light yourself. Time just keeps rolling on.
Again though, everyone else at the spaceport will say that the Earth looks four years, five-or-so-months old.
So it’s a good thing that travelling at light speed is probably impossible, right?
IT’S ALL RELATIVE
Thing is, time dilation occurs no matter what speed you travel. It's just that at today's usual speeds, the dilation is immeasurably small.
Yet as soon as you accelerate away from a “rest frame” (for all currently living humans, that rest frame is "standing still on the surface of the Earth"), time will start to pass very slightly faster for you… at least, as observed by people still on Earth. Ugh. Don’t worry, it makes our brains hurt too.
You can't feel this happening. Because no matter where you are or how fast you are going, a minute will always be as long as a minute... to you. Once you stop the spaceship and get out (or rather, decelerate back to a more sensible speed), only then will you'll realise everyone else experienced
more minutes, more time, than you did. Feel free to go and have a little lie down now and come back to this in a few minutes… we certainly did while writing it.
At the speeds we can manage with our current technology, time dilation is barely detectable. (And because the universe seems to abhor simplicity, there’s also a reverse effect caused by being closer to the centre of a big gravity well like the Earth… strong gravity speeds time up, and that's why - no wait, let’s leave that for another discussion).