From: Phil Goetz (email@example.com)
Date: Sat Aug 27 2005 - 13:39:37 MDT
--- Michael Wilson <firstname.lastname@example.org> wrote:
> Phil Goetz wrote:
> > I think it's interesting that, were one to build a simulation of
> > a universe, it would be impossible to use Newtonian physics.
> > First, you'd have roundoff errors for objects moving at
> > very high speeds - but implementing relativity theory
> > could solve that problem.
> On what are you basing this statement? I have some experience of
> physical simulation as I wrote a couple of physics engines when
> I used to work as a professional games developer. If you are
> using an integrative model, i.e. a model with a discrete state
> for every frame, then low speeds are actually much more prone
> to roundoff errors than high speeds, because the distance moved
> each frame is closer to the co-ordinate resolution.
These low-speed roundoff errors are dealt with via quantum mechanics.
In Newtonian physics, different objects have different speeds.
Say you represent them with floating point. A low-speed object
might move at 1.2345*10^-10 m/s. Its speed is known to within
10^-14 m/s. A high-speed object might move at 1.2345*10^8 m/s.
Its speed is known to within 10^4 m/s. Suppose you're simulating
a high-speed spaceships travelling thru the universe. You only
know its speed, and the speed of everyone in the spaceship,
to within 10^4 m/s or so. You're unable to simulate
what's happening on board the spaceship.
In special relativity, everything moves through time-space at the
speed of light. Each object's velocity is specified by a direction
vector in time-space. Interactions between objects with the same
relative speeds can always be calculated with the same degree of
accuracy. I think.
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