Playtesting a Standard Model Game

[TestTubeGames]

I'm looking for people who'd be interested in testing out a Standard Model game I'm developing. (Disclaimer up front: you'd need an iPhone or other such device, since it is a proverbial 'app')

The game is full of puzzles involving electrons, neutrinos, Z bosons, the whole gambit. I'm hoping it can be an easy, approachable way for people to interact with the (oft-intimidating) subject. I'm looking for people to test out the game, and to make sure it is fun AND the science is up-to-snuff. And I KNOW the folks here in the science section can set me straight.

If you're interested in playing around with a beta-version of the game, and helping me work out kinks, let me know. Either reply here, or shoot me a PM, and I'll fill you in on the details. And aside from that disclaimer above... all are welcome, at any level of background knowledge.

Thanks!

[Tass]

Sounds fun. I'm in.

[gmalivuk]

Any plans for this to be an Android app? If it's as cool as Velocity Raptor, I'm definitely up for playtesting.

[wtfxcore]

I'll try it out if you need someone else!

[Qaanol]

You have my sword.

[scarecrovv]

Velocity Raptor

Holy shit. That's awesome.

Sadly, I don't have a smart phone.

[TestTubeGames]

Any plans for this to be an Android app? If it's as cool as Velocity Raptor, I'm definitely up for playtesting.

Thanks for the kind works about Velocity Raptor! Glad to hear you enjoyed it! Here's to hoping the new one (Agent Higgs) is cool too.

No plans at the moment for an Android version. I'm thinking of making a flash version of it eventually (a la V.R.) so everyone can play, regardless of mobile brand... but that's down the road a bit.

[Dopefish]

Wow, velocity raptor. I approve. I shall totally show everyone I can get to a computer that now.

My phone only phones since I'm terribly behind on the times, so I can't help with this unfortunately. When/if you get a flash version of this, I'll be keen to try though.

[drongo]

I'm interested.

[TestTubeGames]

Scarecrovv & Dopefish -

Thanks for taking a look! And Scarecrovv, just so you know, I quoted you to my wife to help justify the time I spent working on it

[Bears!]

I'm definitely interested in testing it. Also, Velocity Raptor is amazing.

[Eternal Questionner]

I agree, Velocity Raptor was brilliant. A 3D version would have been incredible. Just sayin...

I'm doing my best to get your beta, but my (admittedly old) iPod Touch keeps throwing errors. First it thought your certificate was invalid, then it claimed an 'unknown error', and now the server now seems to be overloaded. I'll try again later.

[idobox]

I'd like to test it, as soon as it works on something else than an apple device.

About velocity raptor: everything I know about relativity is vulgarization, but is it normal that the bullets stop hitting the target when you move? it seems to me that this kind of event should happen regardless of your frame of reference.

[scarecrovv]

I'd like to test it, as soon as it works on something else than an apple device.

About velocity raptor: everything I know about relativity is vulgarization, but is it normal that the bullets stop hitting the target when you move? it seems to me that this kind of event should happen regardless of your frame of reference.

I was actually wondering the same thing. In the seen view, it seems like you should see bullets originate at the cannon, and end at the target. If this isn't actually what you'd see, could somebody please explain?

[TestTubeGames]

The bullets were the most difficult part of the simulation, conceptually. And the last thing that I (I hope) got right.

The effect in fact has a name: the Thomas Precession. Basically, when you've got two objects moving with non-parallel velocities (aka your raptor is moving up in the room, the bullets are moving right), then not only do you get a Lorentz boost - a shrinking - but you also get a rotation.

The origin stems right from the Lorentz transformations. Let's use the example where the raptor is running up, and the bullets are shooting to the side. Since the raptor is moving up, to the raptor the room contracts vertically. The gun and the target, which are in the frame of reference of the room, then simply contract vertically too. No tilts or slants, just squished from the top and bottom. The horizontal line connecting the gun and the target stays purely horizontal. So far, so good.

But to figure out how the bullets contract, we have to combine their velocity and the raptor's velocity. So the axis along which the contraction occurs is no longer vertical... but at some angle between vertical and horizontal. Since the bullets contract along an angle, it'll be like squishing your computer screen from opposite corners. What was once a purely horizontal line (the path of the bullets), is no longer purely horizontal.

And that is why, to the raptor, things seem really kooky when the bullets are involved. Now, I agree it flies in the face of intuition. Since, after all, events should (and do) happen regardless of reference frame. Line up a bunch of wine glasses between the gun and the target, they should all break. No matter how you are running. And yet the raptor would see the bullet at a different location than the wine glasses as they are breaking? Weird. If anyone has a great way to explain-away the counter intuitive nature, I'd be glad to hear it. I'm always looking to get a better handle on this confusing topic, myself.

To sum up this long-winded post: while it is surprising from an intuition standpoint... is just a byproduct of two non-parallel Lorentz contractions.

[scarecrovv]

I fail to see how a bullet can break a wine glass without ever coming into contact with it. Not understanding the equations properly myself, I'm not sure what the right answer is. However, since my understanding of your understanding of the equations produces effects without causes in some reference frames (the raptor sees bullets break glasses by not hitting them), then either your understanding is wrong, or my understanding of your understanding is wrong.

I've never studied relativity in a classroom setting, so it's very probable that I've got all sorts of things twisted the wrong way in my mind, but this is how I think it works (please correct me if I'm wrong):

Spacetime is like a (4 dimensional) rubber sheet. An object in spacetime is like a sharpie dragged along the rubber sheet. Each follows a definite path through spacetime. Depending on gravity, and your velocity, you can observe that rubber sheet distorted in all sorts of crazy ways, but the line you drew with the sharpie is fixed, relative to the sheet, and the topology of the sheet does not change. If two lines intersect in one frame of reference, they will intersect in all frames of reference. If the lines traced out by a bullet and a wine glass intersect in the frame of reference of the gun, they will also intersect in the frame of reference of the raptor. They may intersect in a different place, at a different time, but they will intersect, and the order in which the bullet intersects the wine glasses will always be the same.

I think.

[TestTubeGames]

I fail to see how a bullet can break a wine glass without ever coming into contact with it.

...unless of course it is an opera singer.

I'm not claiming that the bullet doesn't come into contact with the wine glass. Just by my understanding, when the raptor is at some arbitrary location... the bullet will look like it is "over here" and the shattering wine glass will look like it is "over there". But to some extent, this is kind of like an optical illusion. For the events match perfectly (in every reference frame) if the raptor is at the same point. When the raptor is far away, the locations appear different due to that Thomas rotation. But if the raptor, at that instant, happens to be running right past the bullet & wine glass, she will agree that those world lines match up.

So the events do match up in all reference frames... but to a distant observer they may appear to be in different places. (Though even they, if they got out their slide rule and computed it out, would agree that the bullet is really coming into contact with the wine glass).

If someone has a better explanation for this, I'd love to hear it. I've never really heard any official way to explain the counter intuitive nature of the Thomas precession.

[douglasm]

The Wikipedia article does a very poor job of explaining what Thomas Precession is, but I'm almost certain you got the bullets wrong - if two objects are in the same place at the same time, then everything I know about relativity says that this simple fact is completely frame-invariant no matter what velocities the objects might have. If the bullets aren't appearing at the cannon and disappearing at the target, then your implementation cannot be correct.

[Aiwendil]

I assumed that the bullets originating from a point other than the gun and disappearing at a point other than the target was a glitch. If not, it's definitely incorrect. If a bullet is fired from a gun, then all observers, in all reference frames, will see it come from the gun. And if it hits a target, all observers will agree that it hit the target. They'll disagree on when it hit, and what angle it approached from, and at what speed it hit, but they'll agree that it hit.

[TestTubeGames]

A continued thanks to everyone who has offered to help out with testing. I think I got in touch with everyone who expressed interest so far.

And I'm also glad my previous game is eliciting some debate. I posted a thorough explanation of why the bullets behave the way they do on my site (an expansion of what I had above... but with pictures, and comically long). If you're interested, you can give it a read. The short and long of it is that with nothing more controversial than Length Contraction... one can easily arrive at the result. Near as I can tell, with very few steps in the reasoning process, you get yourself some diagonal bullets.

Now of course, if there are any problems with the steps there, please do let me know. My first concern is the science of the game.

(As a completely separate venture, I've been pondering why this IS so counter intuitive, and does seem to fly in the face of some basic relativity rules-of-thumb. Not entirely sure... but I'm wondering if it doesn't have to do with competing definitions of 'Observer.' Originally, Einstein used 'Observer' to mean literally a person at some place, with some speed. But many others use 'Observer' nearly interchangeably with 'Frame of Reference.' The former has a precise location, and might just be able to make local 'measurements'. The latter doesn't have a defined location, and is clearly quite different. Maybe this is where the confusion arises?)

[Twistar]

I don't know about the bullets. In real life it would not happen the way it does in the game. If a bullet hit a target it would look like it hit a target. the bullet hitting the target and the target being hit are the same spacetime event.

I think the issue might be that you're trying to treat the path of the bullets as the object when you need to be treating each bullet individually. Imagine the raptor is standing still (right of the bullets in the center of their path) and the bullets are shooting from bottom to top. If the raptor moves to the right with velocity v he will see the gun and target length contracted in the horizontal direction. Now, I turn to my relativity book (Griffiths E&M in this case..) to figure out the velocity addition formulas.

u_x ' = \frac{u_x-v}{(1-\frac{vu_x}{c^2})}

in this case u_x is 0 so the bullets will ALL take on a velocity of -v, the same as the gun and the target. In short what the raptor will measure is that the whole line of bullets, gun, and target will be moving to the right with velocity v as we would expect classically. Now lets turn to the y direction

u_y ' = \frac{u_y}{\gamma (1-\frac{vu_x}{c^2})}

Now, the bullet's velocity in the y direction (their original direction of travel) will be adjusted. I can't tell this second if it will increase or decrease (maybe depends on if you are moving toward or away from the line) but the speed will change. This is the non-intuitive feature of velocities in special relativity. Even if you move in a direction perpendicular to the bullet's their velocity changes. This is because the distance between the bullets is NOT length contracted, but the time between bullets is time dilated. However, there should be nothing funny happening in the x direction.
If the raptor moves only in the y direction then it will appear (as far as I can tell) the same as it does in the game. The bullets will speed up or slow down depending on which direction the raptor runs. However, and correct me if I'm wrong, but once the raptor overtakes the bullets and is moving faster than them should they not begin to length contract towards eachother again?

In the "seen" part of the game it is likely that the bullets will follow some sort of hyperbolic arc from gun to target depending on where the raptor is located and they will move slowest at the apex of the arc closest to the raptor.*

edit: again, I think the problem is that you're looking at the entire path of the bullets as being length contracted along some wonky angle. The issue is you're trying to approach the whole issue using only length contraction when you need to consider the velocity of each individual bullet and apply the proper velocity addition formulas. Your statement
"So the axis along which the contraction occurs is no longer vertical... but at some angle between vertical and horizontal. Since the bullets contract along an angle, it'll be like squishing your computer screen from opposite corners. What was once a purely horizontal line (the path of the bullets), is no longer purely horizontal."
Seems dicey. My computer screen shouldn't be getting squished. Something should be happening to what the bullets are doing.

*edit 2: This is just a guess, It's definitely possible that this is wrong, however I stand by my and other's statement that the bullets should start at the gun and end at the bullseye no matter what, even in general relativity.
(Now how about a quantum version where you crank up \hbar and the bullets diffract when they hit a slit?)

[TestTubeGames]

I think the issue might be that you're trying to treat the path of the bullets as the object when you need to be treating each bullet individually.

There should be no difference. If you like, instead of bunch of separate bullets, imagine a ruler with a bunch of bullet-shaped-dots on it flying by with the same velocity. The same arguments would apply.

...the bullets will ALL take on a velocity of -v, the same as the gun and the target. In short what the raptor will measure is that the whole line of bullets, gun, and target will be moving to the right with velocity v as we would expect classically. Now lets turn to the y direction...

The room, the gun, the target, all only and exclusively have components of velocity in the x-direction (in your example). The bullets, as you state, also have a component of velocity in the y-direction. Even when the raptor is standing still, there is length contraction for the bullets in the y-direction. The bullets are moving that way. So the frame of the bullets (with a stationary raptor) would be length contracted.

Now that the raptor is moving to the right, the bullets also have a component of velocity in the x-direction. We cannot simply length-contract the bullets in the x-direction now and call it a day. (Though I can apparently verb some nouns). If we did, the reference frame of the bullets would be contracted both vertically AND horizontally. It would be smaller in every which way.

But length contraction only happens along the direction of relative motion. Perpendicular to that, there is no contraction. A textbook flying across our screen at an angle doesn't contract first along the x-direction, then along the y-direction, all-the-while staying rectangular. It contracts along the direction of motion only, becoming some kind of parallelogram.

...but once the raptor overtakes the bullets and is moving faster than them should they not begin to length contract towards eachother again?

Spot on. They do in fact behave that way, though it can be tough to tell. The bullets are going pretty fast, and so by the time you overtake them, you are generally just about to hit the other wall. In level 7, though, they are going slow enough (and the level is basic enough) that if you start on the left and run full-bore to the right, just before you hit you'll notice a wee bit of contraction again in the bullets.

Your statement "So the axis along which the contraction occurs is no longer vertical... but at some angle between vertical and horizontal. Since the bullets contract along an angle, it'll be like squishing your computer screen from opposite corners. What was once a purely horizontal line (the path of the bullets), is no longer purely horizontal."
Seems dicey. My computer screen shouldn't be getting squished. Something should be happening to what the bullets are doing.

Instead of a computer screen, just imagine the ruler I mentioned before. Make it more square if you like, to match the dotted-line image I drew. There is nothing special about the bullets... they just happen to be in some reference frame.

(Now how about a quantum version where you crank up \hbar and the bullets diffract when they hit a slit?)

I know, wouldn't that be something? I'd love to do a quantum mechanics game at some point, though I'm still toying with the best way to do it. Relativity, as advanced and 'modern' as it is, doesn't hold a candle to QM in the difficult-to-physically-represent category. Maybe just a blank screen....... until the wave function collapses to "won" or "lost."

[douglasm]

A little google searching turned up what seems a much better explanation of what Thomas Precession is than Wikipedia has, on page 7 of this pdf:

If this explanation is correct and my understanding of it is correct, then it has nothing whatsoever to do with what the bullets' velocity - it's something that would be involved in the process of figuring out what the room would look like if the raptor were moving diagonally and you were doing the computation by splitting the velocity into x and y components and calculating with each separately in sequence.

[SU3SU2U1]

With the bullets in velocity raptor did you account for time dilation in the frequency of how often they are fired?

[TestTubeGames]

A little google searching turned up what seems a much better explanation of what Thomas Precession...

Ah, that seems right. Then I guess I haven't come across a name for this strange effect, after all.

I thought Thomas Rotation/Precession fit the bill for an explanation here, since it deals with non-collinear boosts (the bullets are boosted in a different direction than the room), and you end up with a rotation (the path of the bullets seems rotated from what one might originally expect). But it may well not be the right name for this phenomenon.

I've been looking around for some formulation of this effect (something like a "bullet and wineglass paradox"), but I still haven't found one. It is simply based on length contractions... so unless anyone spots a problem with the explanation that I had written up on my site, it will be true. And I'm sure we can all agree it is counter intuitive.

With the bullets in velocity raptor did you account for time dilation in the frequency of how often they are fired?

Yes. The bullets from a single gun are in fact all treated as being in the same reference frame. Just a long line of stationary bullets (from their perspective) spaced evenly. There is a cutoff on either end of the line of bullets (so I don't display those which have already hit the target, or those not-yet-fired). To determine where that point is, yes, the program takes relativistic timing into account.

[Aiwendil]

I've only glanced at your explanation, but I suspect you've done something wrong in applying the length contraction. When you combine the two length contractions, you seem to end up with a large length dilation for, say, the distance between the target and a bullet that's about to hit it. But length dilation can't happen in special relativity.

As another argument that this can't possibly be a real effect, one might point out that light emitted from the bullet and the target at the moment of impact would have to reach the raptor at the same time, because they started from the same point in space-time and are both travelling at the relativistically invariant speed of light. (Incidentally, does the effect occur in the "seen" view as well as the "measured" view?)

[scarecrovv]

As another argument that this can't possibly be a real effect, one might point out that light emitted from the bullet and the target at the moment of impact would have to reach the raptor at the same time, because they started from the same point in space-time and are both travelling at the relativistically invariant speed of light. (Incidentally, does the effect occur in the "seen" view as well as the "measured" view?)

The effect does occur in the "seen" view. Start level 34 (for example), and click seen. The bullets look like they disappear a significant distance from the target.

[douglasm]

I've been looking around for some formulation of this effect (something like a "bullet and wineglass paradox"), but I still haven't found one. It is simply based on length contractions... so unless anyone spots a problem with the explanation that I had written up on my site, it will be true. And I'm sure we can all agree it is counter intuitive.

After thinking about this for a bit, I think I know where you went wrong - instead of including Thomas Precession, you left it out. It's just an idea, I don't know enough about the principles and math of relativity to be sure, but I suspect that Thomas precession actually is applicable to this situation and that applying it properly would rotate the line of bullets to line up with the gun and target again.

To explain in a little more detail what I think is going on:
You're storing the bullet position and velocity data internally in the room's frame. That's one boost already. Then you apply another, as you explain on the page you linked. This second boost is in a different direction than the first, so the Thomas precession effect requires an additional rotation calculation to get the final result correct, and you're not doing that extra step. The error is either that you didn't realize the internal data representation already included one boost for the bullets or that you didn't realize the Thomas precession effect requires an additional computation step rather than being merely descriptive and explanatory.

[TestTubeGames]

First off, I'm having a lot of fun discussing SR with all of you. It has been a while since I've been surrounded by physics-minded folk (aka college), so it is refreshing. Thanks for all your interest!

The effect does occur in the "seen" view.

Nice! You're cruising through the game (and not letting Professor Rex get you down ) Indeed, the same type of displacement happens in the seen view, though there it (and everything) is much stranger, so it tends to be more extreme. There are some bonus levels I added at the end that distill down the interesting stuff we're talking about. The second bonus level (scroll to the far right of the level select pages) is unlocked when you beat level 6. It has a bunch of cannons in it with different directions, and you can do the 'measured' or 'seen' view.

After thinking about this for a bit, I think I know where you went wrong - instead of including Thomas Precession, you left it out.

So you're suggesting after the aforementioned length contraction, I should rotate things so it all fits together? I had to think about this for a while (and read up on, and get thoroughly re-confused about Thomas Rotation/Precession), but I think I have an example to show this method wouldn't work. Instead of calculating it all out... this being science after all, I decided to do a test.

My thought was that no matter how much you rotated, you couldn't get the world to line up (in the way people seem to be suggesting). With just one line of bullets, sure, you could go in by hand and line them all up with some rotation and translation. But how about with two parallel lines of bullets? Could you line both of them up at the same time?

I put together a special version of the game with a special level. It has several cannons all lined up, shooting lines of bullets. All the rows of bullets are in a single 'moving' reference frame. You can run around, then pause the game, having the world rotate to see if things can match up. As you'll see, due to the length contraction the bullets go through, their lines are (in general) closer together than the lines on the ground. So you won't be able to place them all correctly.

My sense is what we're seeing may seem odd, but doesn't really fly in the face of expectations. The bullets never truly deviate from their paths. (The functional way to determine they did would be to get struck by a bullet, while not standing on their path-in-the-room. No observer in any reference frame can do that. By all means, run around and try.)

And a note to the method of bullet-placement. The info for the bullets is not stored in the room's frame. Instead it is stored in the raptor's frame. So there aren't two boosts before it is displayed, just one. (Early on I tried it the other way around... but the math and coding got horribly convoluted. This way is much more straightforward.)

[Twistar]

Ok, here is maybe a contradiction. Level 9. Imagine there are walls above and below the bullets. I.e. there is a gun on the right and target on the left but there are walls "containing" the bullets. When I move around I will see the bullets fly into the upper region of the level, but the walls I just described will morph the same way as the gun and target. In fact, I will see some bullets going through the wall. This probably is already happening in other levels. This is no more troubling than the bullets missing the gun or target but it is maybe more striking. If I measure a bullet and wall to be in the same place I would conclude the bullet hit the wall.

I'll keep thinking about what I think is wrong with the explanation on your webpage. I'm quite sure it has to do with the fact that you morph the entire frame of the bullets. Here's what I want to say but I can't fully justify it:
Even if length contraction is supposed to happen in the direction perpendicular to the bullets' motion it shouldn't change anything because the path has no length in that direction, it is a one dimensional line and can thus only be contracted along its length. The bullets themselves are two dimensional and they should be squished accordingly, but their path should only be contracted along it's length.

The picture I dislike is the one with the path and the white background outline. I know you say you don't need to imagine that box being there, but I think this image is what is making the whole thing weird. I'll think about it more.

[nitePhyyre]

From our frame of reference, the bullet moves from the point of the green arrow to the point of the blur arrow instantly. ie: the bullet travels the length of the purple line at infinite velocity. This is obviously incorrect.

Think what would happen if your game had boxes travelling down a conveyor belt instead of individual bullets.

[TestTubeGames]

Imagine there are walls above and below the bullets...

I like it! In fact, I think that would have made a nice level for the game. It would make very explicit the fact that even though it may seem like the bullets pass through the wall... that is just an 'illusion' of your vantage point. As you got closer you'd see they were inside the channel as they should be. (That's my sense of what's happening, at least).

I'll keep thinking about what I think is wrong with the explanation on your webpage.

Please do. I have no doubt now that with all the thought and care we're giving to this, by the end we'll flesh this out in unprecedented clarity.

From our frame of reference, the bullet moves from the point of the green arrow to the point of the blur arrow instantly. ie: the bullet travels the length of the purple line at infinite velocity. This is obviously incorrect. Think what would happen if your game had boxes travelling down a conveyor belt instead of individual bullets.

You are suggesting infinite acceleration, which in the real world wouldn't be the case. And I'm not saying anything mechanically is happening to the bullet to shift it from the "track" to "off the track." Again, I think this is kind of an illusion of our observer's vantage point. And if nothing is really moving from place to place anyway, then speed isn't really an issue.

A conveyor belt (if we ignore the fact that it has to wrap around) would just be like a solid path of bullets. It would move along, disappearing where you arrow points (given that reference frame that observer's location). Again, maybe it is best to think of this as some kind of illusion. Any local observer making a measurement at the target (in any reference frame) would agree that the bullets hit dead on. And measurement is key in relativity. I can't just say a train is shortened because I look down it and eyeball it... there is a very clear functional definition of how one could measure length, for instance. (Involving synched clocks and all that). Perhaps, in the same way, a raptor can't just look across the room casually and be sure two events happened at the same place and time...

[Qaanol]

TTG, are you arguing that you think the Velocity Raptor game shows the bullets correctly? If so, you are objectively wrong. The bullets must follow a straight-line path between gun and the target, and the apparent (seen) shape of that straight line would be exactly the same as the shape of a straight wall or tight rope from the gun to the target.

If two events occur at the same (x, y, z, t) as each other according to one observer, then they occur at the same (x′, y′, z′, t′) as each other according to any other observer. Since “gun fires bullet” and “bullet leaves gun” are at the same Minkowski-space coordinates in the gun’s frame of reference, the same holds for every other frame of reference. Ditto for “bullet hits target” and “target is hit by bullet”.

You can imagine a whole line of “tissue paper targets” on the straight line from the gun to the target, stationary with respect to the gun and target. Maybe these targets are all hanging from a tight wire between the two. In any case, they absorb negligible momentum, so the bullets maintain full speed passing through. Now the events “bullet hits paper target 2,048” and “paper target 2,048 is destroyed by bullet” are at the same (x, y, z, t) as each other in the frame of reference of target 2,048, so they are at the same location and time as each other in every other frame of reference.

Notably, photons from paper target 2,048 as it gets shredded, and photons from the bullet as it punctures paper target 2,048, will follow identical paths at the same speed, so they will reach the dinosaur simultaneously (according to all observers, though they may disagree on the specific time) from the same direction (according to all observers, though they may disagree on the specific direction) so the raptor will see the bullet and the target in the same location at the same time, for every single one of the paper targets filling the space along a straight line (in proper rest frame of targets) between the gun and the target.

[TestTubeGames]

It seems a lot of the arguments here would be far more widely reaching than intended. Suppose we aren't concerned about three reference frames anymore, just the usual two. (In the following examples, the relative speed v=.866c - set to be such that gamma is two. Things contract to half their length.) The raptor is standing still on an 'x' on the ground. 100 feet away from that 'x' is a stationary wall. Some questions:

1. The raptor starts running towards the wall at velocity v. How far away should that wall be in the raptor's frame (and thus drawn on the screen)? (a) 100 feet away still, or (b) contracted to 50 feet?

Answering (a) would imply a Newtonian world. No length contraction, etc. Answering (b) would make sense to me, from a relativistic perspective. Length contraction in the direction of motion.

2. Barely after leaving the 'x', the raptor comes to a full stop. Where does the wall appear to be now? (a) 200 feet away, (b) 100 feet away

This is an easy one. Since the raptor (or equivalently the room) slowed down, length contraction will be undone. Things should double in length... so it will be at (b) 100 feet again.

3. The raptor is standing still on the 'x' again, and remains still. On the wall there is a cannon, aimed at the raptor. It fires a bullet directly towards our hero at speed v. Where should the bullet first appear in the raptor's frame? (a) 100 feet away, or (b) contracted to 50 feet away.

Many of you seem to be arguing for (a). After all the cannon is 100 feet away, so the bullet has to appear there. But there is a direct analogy between this and the first question. If the moving wall appears closer, the moving bullet should, too. So, again, the answer should be (b). If you're still not sure, let's add another part to the question:

4. There is a pane of bulletproof glass directly in front of the cannon. So, just moments after being launched (and traveling a negligible distance) the bullet stops again. The bullet, the glass, the raptor, and the cannon are all in the same reference frame. Where is the bullet now? (a) 200 feet away, (b) 100 feet away

So the bullet was in a contracted frame, and comes to rest in the raptor's and room's frame... In complete equivalence to question 2, we should expect the bullet to appear twice as far away as we answered for question 3. (a) is clearly absurd... there are no relativistic effects to think about with this question... so how could the pane of glass have stopped a bullet 100 feet away from it? (b) makes sense from not only an intuitive standpoint, but also when doubling our result from question 3.

And just to be entirely clear:
5. A T-Rex is standing still next to the cannon through all these experiments. Zero feet away from the cannon. Where would the bullet first appear to him?

Just as with question 3, we can length-contract the frame... 0/2 = 0... so the T-Rex sees the bullet in the same locale as the cannon. (This is why I think we're implying a local observer any time we discuss two events happening at the same place and time.)

...photons from the bullet as it punctures paper target 2,048, will follow identical paths at the same speed, so they will reach the dinosaur simultaneously (according to all observers, though they may disagree on the specific time) from the same direction (according to all observers, though they may disagree on the specific direction) so the raptor will see the bullet and the target in the same location at the same time, for every single one of the paper targets filling the space along a straight line (in proper rest frame of targets) between the gun and the target.

You're argument seems to be that because of identical the photon paths, all observers will see the events overlap. That isn't the case. Check out http://www.spacetimetravel.org/ to learn about the weird warpy world of seen relativity. They have good descriptions of how when we view a non-co-moving reference frame, it will bend and curve. A bending path of bullets wouldn't line up with a straight path no matter what one did. I think there are some Newtonian assumptions underlying your argument as it stands.

[Sizik]

3. The raptor is standing still on the 'x' again, and remains still. On the wall there is a cannon, aimed at the raptor. It fires a bullet directly towards our hero at speed v. Where should the bullet first appear in the raptor's frame? (a) 100 feet away, or (b) contracted to 50 feet away.

Many of you seem to be arguing for (a). After all the cannon is 100 feet away, so the bullet has to appear there. But there is a direct analogy between this and the first question. If the moving wall appears closer, the moving bullet should, too. So, again, the answer should be (b).

You're misunderstanding/applying length contraction. Length contraction doesn't mean "things that are moving appear half as far away as they would if they were still", it means "things that are moving appear half as long as they would if they were still." Thus, in question 1, since the room is seen as moving, it appears half as long, so the opposite wall is only 50 feet away. The bullets in question 3, however, would only look like they were squashed to half their size, not look like they suddenly appear 50 feet from the cannon.

[TestTubeGames]

You're misunderstanding/applying length contraction. Length contraction doesn't mean "things that are moving appear half as far away as they would if they were still", it means "things that are moving appear half as long as they would if they were still." Thus, in question 1, since the room is seen as moving, it appears half as long, so the opposite wall is only 50 feet away. The bullets in question 3, however, would only look like they were squashed to half their size, not look like they suddenly appear 50 feet from the cannon.

But imagine in the first question that on the wall you have a bullet sitting at rest (wrt the wall). If the wall appears closer, of course the bullet will, too. Then remove the wall and just leave the bullet floating there. Then remove the floor. Remove the rest of the room entirely if you wish. At what point would you argue it stops appearing closer to you?

[Sizik]

The point at which it passes me and starts travelling away from me, of course!

The bullet/wall never appears 50 ft. from the raptor when the raptor is moving at a constant velocity. When he's standing still, they're 100 ft. away. When he's moving, they're 50 ft. away from the X that the raptor was standing on before he accelerated to his current velocity (there's a point during the acceleration where the wall/bullet will look 50 ft. away, but that doesn't matter).

[TestTubeGames]

Made me laugh... that's my kinda humor (though I guess we all are here due to shared taste in that matter)

We can, in the example, take acceleration out of the picture entirely. Change the exact wording to "The raptor (starting and accelerating somewhere behind the 'x') is running at constant v towards the wall, then looks down and notices she is just passing the 'x'..." So we're back to just straight-up velocities.

[Sizik]

At that point then, the bullet appears 50 ft. away from the raptor.

The same would thus apply to the 3rd question: when the raptor reaches a point 50 ft. away from a bullet, it appears to be 50 ft. away.

[douglasm]

I'm gradually getting convinced that the length contraction is correct, but I firmly believe that the final result is wrong and there is some other factor you're missing that would compensate for it.

Ok, new idea: If the raptor is moving down, then in center view (the one where the raptor is always in the same position on the screen) the bullets should be moving diagonally up. I have tried this in the special level, and the bullets do move upward, but the vertical component of their velocity is nowhere near high enough. I know the bullets' already high horizontal speed means the relativistic velocity addition formula would reduce that effect, but I looked up that formula and the reduction is nowhere near enough to match what I see on screen. I measured the bullets as moving at 2.4 mph, or .8c, by matching velocity with them. Yet even when I'm moving vertically at speeds even higher than that, the bullets are barely creeping along at all vertically. Their vertical speed is so small, in fact, that I had to hold a ruler to the screen (calibrated by matching to one of the lines while at rest) to be sure it was there at all. It's too high to be a rounding error, unless both you're using a lot lower-precision variables than you should and it's getting compounded through multiple calculation steps, but I'm not sure what else could explain it. In any case, it is clearly incorrect.

I think that in addition to the length contraction you're applying, you also need to adjust the slope of the lines to account for velocity addition.

About the special level, it would be a lot easier to test ideas with high speed stuff if not for the level's small size. Could you try making the special level infinite, with an infinite array of cannons? Also, a key to hide the room to make focusing on the bullets easier would be nice.