Trace out a random walk (Brownian motion, but bounded within the confines of the galaxy), accelerating towards c so that the proper time elapsed is bounded. In particular, accelerate such that when the galaxy reaches an age of infinity, you have only aged by one hour. Now, probabilistically you should collide infinitely often with absolutely everything, including your buddy, within one hour of proper time. This also works in a two-dimensional unbounded universe, but not within a three-dimensional unbounded universe. Sincerely, Adam P. Goucher
----- Original Message ----- From: Dave Dyer Sent: 02/01/14 06:35 PM To: math-fun Subject: [math-fun] physics thought experiment
You and your buddy have each woken up at some random, unknown point in the milky way galaxy.
You have a very bright, omni-directional beacon that can easily be seen from any point inside it's light cone.
You can travel in any direction, at any speed up to C (but not exceeding it of course).
Your goal is to locate and rendezvous with your buddy for one last drink, sometime before one of you dies of old age.
What's your strategy.
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