Yakk wrote:I had an amusing thought.
Given that you have a perfectly focused laser sail that is pumping out X power at a frequency of lambda (does this matter?), and you have a perfectly efficient, perfectly reflective light sail, and your ship has mass M, how fast can you get going? Is there a limit?
Now, if you managed constant acceleration, clearly there would be a limit on how much power you'd get (the even horizon would form behind you). But as your power input falls, so does your acceleration, making the event horizon fall back further and further.
If your laser is perfectly focused, your power won't decrease from distance, but it might due to redshift. Even so, each photon would give you a little bump, so you'd continue accelerating without end (obviously staying under c) if there wasn't anything slowing you down. At high accelerations, you run into a heat bath from the Unruh effect, but that shouldn't come into play here, as the accelerations are low. However, even discounting inter-planetary/stellar/galactic gas and dust, you still have to contend with the cosmic background radiation, which isn't in the microwave spectrum anymore now that you've blueshifted it with your enormous velocity. How big that effect is will depend on how long you've been accelerating while the Universe expands and lowers the energy of the background photons. Come to think of it, GR redshifting is going to affect your laser too, if your thought experiment goes on long enough.
Eventually you'll be outside the observable universe of the laser source due to the expansion of the Universe. A constantly accelerating body in a static universe will have a horizon too, but your acceleration is decreasing, and that makes it complicated/contingent on details/etc.