Sean (the other Sean) said,

“In fact, if we had a giant acceleration/thrust the whole game-verse would contract to thin line instantly, then propagate at nearly the speed of light once we let up an the accelerator.”

This post is called,

“Cancelling Myself Out of an Equation” or “How to Incorporate Yourself Into a Law of Physics, Then Out of It Again, Or In It Again, Depending On Your Point of Reference”.

If it takes all of the universes energy to fuel a giant -acceleration/thrust- to nearly the speed of light to go into a line, might it not be reasonable to turn our attention to SR’s causal terms for,

“ok, we ave fuel mate, now u do the thrust cos this is the order, innit, geddit?”

Consequently, in this instance, the universe disappears before it has a chance to be a result of it being used up for itself, thus cancelling itself out. This immediately eliminates the universe, so it’s now gone (now that’s more balanced than my wall shelf) and a chance of an observer being there watching the job (the observer is part of the universe so therefore fuel) thus evokes complete and utter obliteration of being able to explain the thought experiment in the first instance.

Result: observer is cancelled out of itself as a result of the thought experiment by the thought experiment.

Conclusion.

Don’t think of experiments, do them, or summat…

P.S I love the American TV Show “Big Bang Theory” ! ! !

Claire

“In fact, if we had a giant acceleration/thrust the whole game-verse would contract to thin line instantly, then propagate at nearly the speed of light once we let up an the accelerator.”

This post is called,

“Canceling Myself Out of an Equation” or “How to Incorporate Yourself Into a Law of Physics, Then Out of It Again, Or In It Again, Depending On Your Point of Reference”.

If it takes all of the universes energy to fuel a giant -acceleration/thrust- to nearly the speed of light to go into a line, might it not be reasonable to turn our attention to SR’s causal terms for,

“ok, we ave fuel mate, now u do the thrust cos this is the order, innit, geddit?”

Consquently, in this instance, the universe disappears before it has a chance to be a result of it being used up for itself, thus canceling itself out. This emmedietly eliminates the universe, so it’s now gone (now that’s more balanced than my wall shelf) and a chance of an observer being there watching the job (the observer is part of the universe so therefore fuel) thus evokes complete and utter abliteration of being able to explain the thought experiment in the first instance.

Result: observer is cancelled out of itself as a result of the thought experiment by the thought experiment.

Conclusion.

Don’t think of experiments, do them, or summat…

P.S I love the American TV Show “Big Bang Theory” ! ! !

Claire

Ralph,
You’re right about the weirdness of the periodic boundary conditions. They’re good for game play, but they do confound the physics lesson a bit. We’ve tossed around a few ideas about how we could change that, e.g., introduce a contracting hard boundary, but decided to stay close to the original game. As it is, accelerating in the ship’s frame, draws in more space through the period boundaries. I guess we should think about it as expanding and contracting a 2-D closed space. (see http://two-sheds.blogspot.com/2008/03/prepare-to-be-blown-away.html)

If it’s a proportional effect, what sets the acceleration scale when the only constant in (special) relativity is c?

The size of the ‘boost’ sets the acceleration scale. It’s exactly as you say, nothing but applying the equations of SR (Lorentz transformations and relativistic velocity addition). In the game when you thrust, you boost to a new reference frame and all distances contract. If that boost is large enough, as in our game, the contracting effects due to the boost can exceed the progress due to the velocity. Tuning the thrust/boost continuously lower decreases this effect until it’s not noticeable.

I’d like to go point-by-point and deal with your concerns, but I fear hijacking this thread and I don’t want to wear out my welcome. Anyway, it’d probably help if we put the source code up so you can judge for yourself. But first I should probably consult my collaborators… also make sure there’s a comment or two in there.

I’m not sure what you mean by “proper time on the ship slows down”.

Ok, I was a bit confused. When moving close to the speed of light the relative velocity between the ship and the asteroids should be c. But the time it takes for the ship to reach the next asteroid in the ship’s reference frame should be shorter than in the “lab” frame, a la the twin paradox, and I wasn’t seeing that in the game. Length contraction actually takes care of this: the asteroid is still passing by at (nearly) the speed of light, but the distance between the ship and the asteroid is length contracted, so the there is a smaller distance to cover. That contraction keeps happening the more you accelerate, even if the relative speed isn’t changing at all. So if the ship were travelling through an infinite field of asteroids, they would pass by faster and faster in the ’ship” frame. Moving at the same speed, but getting closer and closer together.

Perhaps this is masked by the way you’ve done the boundary conditions, where the universe effectively gets bigger the faster you go?

No, I believe that behavior is correct. The amount that the asteroids appear to “stop moving” is a function of the acceleration.

I disagree here. Why do you think there should be a discontinuous change between accelerating and non-accelerating states? That doesn’t make any sense to me. What happens to the discontinuity when the acceleration becomes arbitrarily small? If it’s a proportional effect, what sets the acceleration scale when the only constant in (special) relativity is c? My recollection is that one just integrates the SR equations from the instintaneously co-moving inertial frames to handle acceleration. That will give you smooth (and monotonic) changes as you turn the drive on and off.

I guess it wouldn’t be very interesting if you just showed the whole universe contracting to a line, but I think it would be more accurate. Are you somehow spreading the asteroids back out to fill the now-larger universe once the ship reaches a new constant velocity?

I guess it is difficult to represent the length contraction of the universe with periodic boundary conditions.

Ha! Right you are. Also, I like your idea about making the edges blink. We’ll change that.

But in the “ship” frame, shouldn’t the asteroids keep speeding up as gamma increases and proper time on the ship slows down?

I’m not sure what you mean by “proper time on the ship slows down”.

In any case, something’s definitely wrong in the “ship” frame under acceleration because the asteroids all stop moving and then jump back to a different place and blink phase when acceleration stops.

No, I believe that behavior is correct. The amount that the asteroids appear to “stop moving” is a function of the acceleration. In fact, if we had a giant acceleration/thrust the whole game-verse would contract to thin line instantly, then propagate at nearly the speed of light once we let up an the accelerator.

Thanks again for the input. Maybe we’ll put up a FAQ? But then again, making the game is more fun than explaining it.

Ok, I can see the blink rate decrease with relative speed in the “ship” frame if I reduce the speed of light to 1.0. It’s hard to tell otherwise because everything gets contracted to a line and the edges don’t blink. I think I can also see a change in blink rate with relative velocity of the asteroids in the “lab” frame at c=1.0. That’s definitely wrong if true.

But what I meant about time dilation is that while in the “lab” frame, the ship tends to a limiting velocity under constant acceleration. But in the “ship” frame, shouldn’t the asteroids keep speeding up as gamma increases and proper time on the ship slows down?

In any case, something’s definitely wrong in the “ship” frame under acceleration because the asteroids all stop moving and then jump back to a different place and blink phase when acceleration stops.

You raise some good points. The game is indeed weird, but the weirdness lies in the physics, and not (I hope) in the software.

When you’re accelerating, the distance (in the direction of travel) between all objects is decreasing continuously. If the boundaries of the game-space were larger and contained more asteroids, you would see more asteroids appearing at the boundaries while you accelerated. These additional asteroids would help you judge your speed a little better. Perhaps we’ll make a version of the game with this mod?

With regard to time dilation, check out the Nine ‘Roid or Sandbox. There, you can see the asteroids blinking at different rates depending on how fast they’re traveling with respect to you. That is of course, if you’re in the ship’s frame.

We worked hard to ensure the game contained only features and not bugs, but I agree that sometimes they’re a bit difficult to distinguish. Thanks for the input.