OK, suppose I wanted to simulate this thought experiment -- perhaps first in 2D (plane of the galaxy). My first thought was to generate "time" segments, in between which all movement was inertial (special relativity). My problem is what to do at each segment end-point where forces are applied and accelerations must be accounted for. I'm willing to keep 2 (or even 3) different clocks, but I'm not sure how to do the update functions. The problem is that for the segment end-points, the accelerations are infinite, but also for a very short time. Normally this is handled by considering impulses of a finite energy, but I'm not sure what to do with the quite large effective masses of humans travelling at very near light speed. In any case, simply doing the computer simulation would finally teach me how GR really works in this instance. At 02:16 PM 2/2/2014, meekerdb wrote:
How much turning would be required by Brownian motion would depend on some scale factor. But the idea is to keep your speed relative to the galaxy close to c while searching so you'd want to get up close to c and then just turn (i.e. acceleration normal to velocity). So your best search path would be relatively smooth orbits around the galaxy. Physically the problem is that you have to exhaust a enormous mass/energy, even with an exhaust velocity of c, in order to accelerate. So you have to start off with this enormous mass.
I'm not sure how the beacons play into this. You can't just signal one another because the photon round-trip time is long compared to your life time.
Brent Meeker
On 2/2/2014 1:34 PM, Charles Greathouse wrote:
Well, about a year with (Newtonian) acceleration = g, and about 5 years with proper acceleration = g. But I think the problem is turning -- Brownian motion would require far more turning than you could afford at that slow pace, and even an acceleration-limited modification would probably require much more acceleration than you could afford within your lifespan. (Right?)
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Sun, Feb 2, 2014 at 3:02 PM, meekerdb <meekerdb@verizon.net> wrote:
I think even 1g will. It doesn't take long to get to 0.9999.
Brent
On 2/2/2014 6:35 AM, Henry Baker wrote:
Yes, but what if we place a limit of 20g's on the acceleration? Can you still do your random walk? Will 20g's allow you to see the heat-death of the universe?
At 06:27 AM 2/2/2014, Goucher wrote:
Also, Goucher's brownian motion solution is technically wrong in the sense
brownian motion has infinite path length Yes, it does, but you can cover that in finite *proper* time. Admittedly the heat-death of the universe would have occurred in that amount of time, but you would still be alive.
so even if you travel at C and do not mind infinite acceleration, you'll
still never get anywhere. Only from the perspective of a static observer. From your perspective, you'll cover the universe in finite time.