Re: C-ship

[T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden)]

Hello Steve,

>>The problem with John's simulator is that he almost certainly cannot
>>simulate moving objects in the field of sight. For example a rotating disc
>>with radial lines would not show as disc with spiral lines for an observer
>>at rest.
>
>Huh?  As far as I know a disk with radial lines won't show up
>with spiral lines to any observer.  It may appear rotated,
>however.

Yes, that's what I meant. I tried to say that John's simulator probably
would NOT show that.

>I am still trying to get enough understanding of special
>relativity theory to make sure I get things right.  I also want
>to work out more of the mathematical techniques I will use.

Once that is ready, writing the simulator is easy ;)

>The basic structure of the simulation will be to model worldlines
>for all objects, and compute visibility for display by tracing
>light-like worldlines from a observer point to the other
>worldlines in the simulation in some common frame, then transform
>apparent positions of these objects in the common frame into the
>frame of the observer.

Indeed, but for this you need to have a history of all the objects positions.
As long as they move linear or linear accelerated that's not so difficult
because you can use a function. But as soon as the behaviour gets less
simple you may need large arrays and with it come less precise calculations.
Also it would be nice to see the time at every point of the several objects
(for example by halting the simulation and clicking with the mouse).

>I think most of the relativistic effects, particularly things
>like aberration and rotation induced by moving at relativistic
>speed, can come out of fundamental behavior of the simulation
>rather than having to be explicitly calculated in each case.
>Aberration is simply a result of the way worldlines of light rays
>Lorentz-transform.

Rotation will indeed follow from the finite speed of light. But I don't see
how abberation does not show up after the LT of the worldlines. Lightrays
coming form the backside of the observer won't come from the front after the LT.

>Rather than seeing Lorentz contraction, you
>see object rotation, because you see light from farther parts of
>an object that came from it earlier than light from nearer
>parts.  I am trying to prove to myself that all these effects
>will fall out of the simulation model I want to use; so far I am
>pretty confident that I'm on the right track.

This rotation is only seen if the object moves along you, thus not towards you.

>>What I asked John Walker was that I would expect curved lines in the SHUTTLE
>>and FLYTHRU movies. I think this curvature would be result of the finite
>>travel speed of light, ie. light from further objects reach the observer
>>later than the light from nearer object.
>
>That effect should happen.

I've been rethinking this bending of the lines today. And now I think that
the lines should be straight. The lines are only curved if the objects are
moving. If the observer is moving and the objects don't move this bending
will not occur. What do you think after reading this?

This would mean that you could "easely" recognize moving objects because of
the curvature they have and that still objects don't have.

>I think one small mistake he is
>making in his aberration calculations is assuming that all
>objects are effectively infinitely distant for the purpose of
>computing the aberration.

Yes, in a book I read the term "supersnapshot" for that method. 

>The way that I'd end up computing how the line would look would
>be to trace lightlike worldlines from the observer to points
>along the worldlines of points on the line.  The farther parts of
>the line would have worldline intersections that were earlier in
>time than the intersections of points nearer on the line, and
>since the line is moving, seeing a point on the line earlier in
>time means you'd see it earlier in its motion history.

Yes, you need to know the functions of motion several points of an object.
Let's call one point of the object P[t].
Call the point of the observer O[t].
What does the observer see at time T1? The observer sees an object if a
photon that left the object at time T0 reached the position O[T1].

So in formula's:

c*(T1-T0)=Sqrt((O[T1]-P[T0])^2)    c is the speed of light

With this equation one can calculate T0. When knowing that, you can
determine the position of the object at T0, so then you know from what
direction and from how far the photon came.

Do this for all object-points and you have a created the "see-able" world,
after that you could use the c-ship program.

>Your orientation to the line does make a difference, though.  If
>it was moving end-on towards you, then you'd see the line rotated
>rather than curved as a result of the same effects.

Yes, assuming of course that it would not come straight at you, because than
you would see a single point.

>Now that I think about it, simple extensions to POVray for
>modeling relativistic effects probably wouldn't work well,
>because you really have to raytrace in four dimensions to
>properly model them.

Indeed, although it is easy to calculate the length of the lightray, it is
much more difficult to know where all object where in the past.

>On the other hand, an effect he pretty much got right that is a
>little nonintuitive is the appearance of the lattice receding
>during the early period of acceleration; at that time you haven't
>gone very far in the lattice, but aberration is causing the light
>from beside and behind you to begin to appear in front of you,
>producing the appearance of moving backwards in the lattice.
>Only when your proper-to-frame time ratio gets very high does
>moving through the lattice begin to counteract the aberration
>effects. 

Yes, I noticed that effect too. But the formula to calculate the aberration
is quite simple. In raytracing it is very easy to substitute one angle by a
new one.
It is fascinating that at higher velocities the biggest part of the view is
the area that is after you, the part in that normally is in front of you is
reduced a very small circle. 

Timothy