If the universe is 93 billion light years in diameter, how long would it take to travel end to end at light speed? originally appeared on Quora, the place to gain and share knowledge, empowering people to learn from others and better understand the world. You can follow Quora on Twitter, Facebook, and Google Plus.
It would take an infinite amount of time to traverse the universe.
That's because the universe will continue to expand whilst you are travelling, and so there are regions of space which will remain forever sealed off from you — even travelling at the speed of light.
These areas are said to be beyond the 'cosmological event horizon', which sits at a radius:
Where a(t) is the solution to the (nasty) differential equation:
Here H0 is the current-time Hubble Parameter, and the various Ω0 contributions are the density ratios of (from left to right), matter (including dark matter), radiation, the net curvature of the universe, and the so-called ‘dark energy’ term.
At the current time t=13.7bn years, and using the current best measured values of the cosmological parameters, the cosmological event horizon is at a radius re≈16bn light years — which is well within the radius of the observable universe (46 bn light years). Hence, there are regions of the observable universe which are sealed off behind this event horizon.
It's not a coincidence that it's called an “event horizon” — in many ways the particle horizon looks exactly like the event horizon of a black hole (albeit with a suitable coordinate change).
Because of this, you cannot travel to these regions, even travelling at the speed of light, as by the time you get to where they are now, they will have expanded to a point further away. Like Achilles and the tortoise, you will forever be playing catch-up, except this paradox cannot be resolved — its just a violation of our intuition.
It's counter intuitive and horrible, but it is also true.
General Relativity is weird.
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