If two things differ in space, or differ in time, then observers will not agree on their relative locations and times. But if two things are identical in space, and identical in time, then all observers will agree they are the same event. Because they are the same event.
TestTubeGames wrote: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?
TestTubeGames wrote: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
TestTubeGames wrote: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.
The raptor looks at the bullet and says “The cannon and the x are at rest with respect to me, and are 100 feet apart. That bullet is 100 feet away.”
The bullet looks at the raptor and says “The cannon and the x are moving with respect to me, and are 50 feet apart. That raptor is 50 feet away.”
Why do they differ? Because the bullet and raptor are in different locations and different reference frames, so the two points of interest (cannon and x) cannot be in both their frames of reference (they happen to be in the raptor’s frame).
You can read about this effect, where two observers on course for a head-on collision disagree about how far apart they are, in the context of muon decay here (the paragraph after the block quote). The saving grace is that one observer sees the distance as contracted, whereas the other observer sees the time as dilated, in counteracting amounts.
TestTubeGames wrote: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
This is the question you want to think about, because it clearly shows the game is currently wrong. If the game were right, then at the moment of firing the cannon, in the frame of reference of the raptor, the bullet would teleport (or at least go faster than light) to where it first appears away from the cannon, then at the moment of striking the bulletproof glass it would teleport (or go FTL) back to the end of the muzzle. That is clearly impossible, since it requires superluminal velocity.
TestTubeGames wrote: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?
Right at the front of the cannon. And since the T-Rex and the Raptor are in the same frame of reference (rest with respect to the room), they agree on all observations.
In fact, we can let the raptor have a t-rex buddy, and have them communicate a plan ahead of time so that they both move together, always remaining in the same reference frame, 100 feet apart. They can run by the cannon, with the t-rex brushing the mouth of the cannon at the instant a bullet is fired, so the t-rex gets hit. Every observer agrees on this fact, because the t-rex and the bullet are in the same place at the same time.
However, the raptor 100 feet away is moving so the bullets appear in game some distance away from the cannon. And the t-rex is moving at the same velocity as the raptor, so the raptor and t-rex agree on all observations (with some delay from light-speed, but they do agree). That means either a bullet far away from the t-rex struck the t-rex, or the game is displaying things wrong.
TestTubeGames wrote:Qaanol wrote: ...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.
I don’t know what you think that link says, because I don’t see any description there. If you could provide a more specific link to the actual description they provide, or quote it here, that would be helpful. In any case, my argument is entirely correct.
Imagine a pipe or tube of arbitrarily-small diameter, at rest in some reference frame. Let some high-speed particles be fired down this pipe from one end to the other. The particles start inside the tube, they end inside the tube, and at no point do they puncture the walls of the tube. The particles are always inside the tube (quantum indeterminacy notwithstanding).
All observers agree that the particles were fired from one end of the tube to the other, and stayed inside the tube the whole time. No observer sees the particles hitting or passing through the walls of the tube.
Now, for any arbitrary observer, the path through space taken by the high-speed particles is the same as the path through space occupied by the pipe. Observers might disagree on what that path looks like in space and how it curves, but every observer agrees that, whatever the path looks like, both the tube and the particles follow it. Because the particles are inside the tube.