From: Michael Wilson (firstname.lastname@example.org)
Date: Sat Aug 27 2005 - 14:56:05 MDT
Phil Goetz wrote:
> 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.
If you're using variables that have insufficient dynamic range to
encompass the entire co-ordinate space, then by definition you
must be using some kind of system for nesting reference frames.
If you're using true absolute co-ordinates, i.e. every particle
or similar ontological primitive has a position in quanta relative
to the universe itself, then your variables must have enough
range to allow speeds from 1 distance quanta/time quanta up to
1 universe diameter/time quanta without any loss of precision.
Fractional speeds imply that the effects of momentum are
probabilistic if you are using an integrative model; they may
remain deterministic if you are using a continuous model.
Continuous models are more complicated but for relatively sparse
universes (and our universe is very sparse) they are much more
computationally efficient as well as being deterministic
(requiring no external source of randomness).
If storage space and computing time aren't an issue, using
solely absolute co-ordinates is certainly much simpler. That
said note that the difference between representing co-ords in
our universe absolutely using (say) 256-bit integers and
32-bit floats you seem to be using is less than an order of
magnitude, which is pretty insignificent when you start
talking about the amount of computing power needed to run a
direct physical simulation of everything that exists. But anyway,
even if nested reference frames are used, this still isn't an
argument for relativity; indeed relativity is still a massive
complication to the calculation of any interactions, plus you
either have issues with rounding mismatched clocks to time
quanta or you have to abandon the notion of global instantaneous
states entirely, which is another major complication. If
relativity really did simplify anything, all non-trivial physical
simulation programs would be using it, whereas of course in
reality very few do.
* Michael Wilson
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