The Lance Duel Paradox: Who Will Win?

[TumblingDice]

That's right.
However, with a sufficiently lower speed of approach between the two knights (this speed has nothing to do with any reference frames or the speed of any observer - don't be confused by the fact that we might choose to use a reference frame in which one or the other knight is at rest) the result will be only one knight being unhorsed. If the knights are moving slowly enough, the various impacts will be timelike-separated not spacelike-separated, and despite the relativity of simultaneity all observers will agree on their relative ordering.

Thank you for replying, Nugatory. I always understood the lower speed result, and THOUGHT I understood the multiple issues that kept the laws of physics make sense at relativistic speeds for all inertial frames. I remember well the "rigid object" FAQ and took the 'speed of sound' as the max the lances could convey a signal (e.g., move from one end to the other.)

I think that's where I took my left turn in the wrong direction. Since both lances are already each in their own rest frame, they're already in relative motion, so signal wave doesn't apply at all. Except to those who are arguing their points about how soon lances will impale each other...

Others have been trying to define what "win" means and maybe some smoke blowing and hand waving. <big grin>. Hey, when it comes down to a collision of this magnitude, there will be NO WINNERS!

With that said, I've believed this thought experiment has been about simultaneity/dilation/contraction paradoxes from different inertial frames all along. If that is indeed the devil behind the puzzle, then I would think it's really meant as was mentioned much earlier, this is like the bug in the hole watching the approaching bolt. Consider if the tip of each lance made the knight it touched (and their lance and all) vanish, instantaneously. So only one winner...

 

[yuiop]

then I would think it's really meant as was mentioned much earlier, this is like the bug in the hole watching the approaching bolt.

Just for reference here is a cute animation of the bug and rivet paradox. (No bugs were seriously hurt in the making of this animation).

 

[TumblingDice]

Thanks, yuiop. On my droid tablet right now - animation doesn't play but I'll catch on desktop tomorrow.

And I just realized the flaw in my own 'twist' with the vanishing knight on contact. It could be argued that having an entire knight and lance disappear instantly would violate in terms of non-locality, so if fastest all could disappear was at c, both tips would touch knights at relativistic speeds, albeit Sir Shortlance may no longer be at the other end of his, from some reference frames.

I was trying to simplify the important aspects. <sigh>

Hoping I'm not going too far off topic. I hate when that happens to a thread...

 

[PAllen]

I think that's where I took my left turn in the wrong direction. Since both lances are already each in their own rest frame, they're already in relative motion, so signal wave doesn't apply at all. Except to those who are arguing their points about how soon lances will impale each other...

I believe you might be confusing separate discussions about relative speeds such that collision events have spacelike separation, in which case the problem is really trivial, with discussions of "what if speeds are of the order of speed of sound in solids", which is altogether non-trivial.

Others have been trying to define what "win" means and maybe some smoke blowing and hand waving. <big grin>. Hey, when it comes down to a collision of this magnitude, there will be NO WINNERS!

ditto, but there is still a fundamental difference between knights going a thousands of meter per second vs. > 8/17 c. In the former case, an invariant statement can be made about who was hit first. In the latter case, no such statement can possibly be made.

With that said, I've believed this thought experiment has been about simultaneity/dilation/contraction paradoxes from different inertial frames all along. If that is indeed the devil behind the puzzle, then I would think it's really meant as was mentioned much earlier, this is like the bug in the hole watching the approaching bolt. Consider if the tip of each lance made the knight it touched (and their lance and all) vanish, instantaneously. So only one winner...

Nonsense. Precisely because for relative speed > 8/17 c there is no way to say which collision occurred first.

 

[TumblingDice]

@PAllen: Thank you for all of the feedback and information. I need to take some time to digest (and redigest) multiple aspects of my thought process.

When you say, "there is no way to say which collision occurred first.". Well, that's where I thought it depends on what the OP and his friend had in mind when they discussed the premise and possible paradoxes together. In my post #31, I was trying to drill into "there can be only one reality", was thinking too quickly that simultaneity would only become an issue if both lances were equal length in their rest frames. I was looking to tighten the experiment by saying, what if a knight and lance vanished when touched? I thought this would drill closer to the bare metal of the perspective of different inertial frames, but as I posted later, even if a knight began disappearing when touched, the fastest any disappearing could propagate would be at c, and now I realize I'm not helping matters at all.