## Thursday, April 12, 2012

### to infinity and beyond...

suppose you've got a spaceship with amazing engines that are able to provide an acceleration of $1g$ measured inside the rocket, such that you would not notice any difference to living on Earth.

what's the time measured on clocks inside the rocket that would pass while travelling
1. to the centre of the Milky Way?
2. to the most distant quasars we see today?
3. the Hubble distance?

1. All answers can be found here;

http://xxx.lanl.gov/abs/0909.1551

The Adventures of the Rocketeer: Accelerated Motion Under the Influence of Expanding Space

Juliana Kwan, Geraint F. Lewis, J. Berian James
(Submitted on 8 Sep 2009 (v1), last revised 9 Sep 2009 (this version, v2))
It is well known that interstellar travel is bounded by the finite speed of light, but on very large scales any rocketeer would also need to consider the influence of cosmological expansion on their journey. This paper examines accelerated journeys within the framework of Friedmann- Lemaitre-Robertson-Walker universes, illustrating how the duration of a fixed acceleration sharply divides exploration over interstellar and intergalactic distances. Furthermore, we show how the universal expansion increases the difficulty of intergalactic navigation, with small uncertainties in cosmological parameters resulting in significantly large deviations. This paper also shows that, contrary to simplistic ideas, the motion of any rocketeer is indistinguishable from Newtonian gravity if the acceleration is kept small.

2. A rocket in which you feel exactly 1g will obviously stay still on the Earth's surface forever. This is the unique solution assumed the journey starts there.

It's probably better this way because someone who visits the black hole in the center of the Milky Way is unlikely to come out and travel to quasars. Not mentioning that approaching a quasar may be an uncomfortable experience as well.

3. :) let me rephrase the question a bit... we're looking for the time displayed by a clock inside a rocket travelling these equivalent distances using only special relativity for calculating the eigentime.

4. >> :) let me rephrase the question a bit... we're looking for the time displayed by a clock inside a rocket travelling these equivalent distances using only special relativity for calculating the eigentime.

Eigentime? You mean proper time?

And you can't just use special relativity, as in a few years you'd be out in the Hubble flow and need to use a GR metric.

5. yes, i'm sorry - i meant proper time. i'm perfectly aware that one would need to use general relativity at some point, and that's why i tried to clarify the question by saying that i'd like to ask for travel times for the *equivalent* distances, as if the destinations were present in a static Minkowskian space time. but of course i'd be happy to see actual numbers for the more complicated problem of an evolving metric. :)