# What do lance warriors really see when they stab each other?

## Main Question or Discussion Point

I got a strange problem and it is not homework. I am not sure if this problem is low level, but I just can't imagine the whole picture.

Problem:
two lance warriors are going to have a fight. Assume the fight is perfectly fair, the lance and the horse and even the two participants are identical.

let me define the two warriors. One is going to ride the horse and go forward, call him warrior M (it means Moving), another one is called warrior S (it means Stationary) who will not move forward and will wait for opponent to come.
warrior M moves with velocity v towards warrior S (the velocity is relative to the velocity of the venue).
By a frame with velocity v/2, he sees two warriors stab each other at the same time.

Here is the problem, for both warrior, they see the opponent has shorter lance due to length contraction. at the moment they are able to stab the opponent, there is the thing I cannot imagine. M will see that he stabs on S first, but S will also see that he stabs on M first.

Until this moment, everything seems to make sense. HOWEVER, imagine a warrior being stabbed before stabbing opponent, his attack will be different not being stabbed first. For the above example, M stabs on S first, then S cannot make a normal attack on M (normal attack means the attack v/2 frame sees).

So, what will the warriors actually see the opponent's movement???

Attempt of the imagination.
Is it possible to say the warrior M stabs on opponent, however the opponent does not have any reaction (like bleeding or falling from the horse, whatever reaction happens after being stabbed) until opponent stabs on the warrior (same as warrior S)? I think this imagination is ridiculous... Is there a better imagination...? I really want to sleep T.T

## Answers and Replies

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PeterDonis
Mentor
2019 Award
Is it possible to say the warrior M stabs on opponent, however the opponent does not have any reaction (like bleeding or falling from the horse, whatever reaction happens after being stabbed) until opponent stabs on the warrior (same as warrior S)?
These "reactions" take time; in particular, it takes time for the tip of a warrior's lance to change its motion in response to the warrior being hit by the other warrior's lance. So it's perfectly possible for each warrior to unhorse the other.

Nugatory
Mentor
By a frame with velocity v/2, he sees two warriors stab each other at the same time.
It's not going to be $v/2$ that the two stabs are simultaneous - you're forgetting to allow for relativistic velocity addition. That doesn't really change anything here, but you'll have to remember this when you go back and work through the problem carefully with actual math instead of qualitative descriptions.

Is it possible to say the warrior M stabs on opponent, however the opponent does not have any reaction (like bleeding or falling from the horse, whatever reaction happens after being stabbed) until opponent stabs on the warrior (same as warrior S)? I think this imagination is ridiculous... Is there a better imagination...
Warrior M and S both have the exact same experience because of the symmetry of the situation - as far as each one is concerned they're at rest and the other one is approaching them at speed v. For both: The other guy's lance point smashes me in the chest. A moment later I see my lance point smashing the other guy in the chest, and somewhat after that I feel the butt end of my lance kick hard as the shock impact of the tip is transmitted down the shaft to my hand.

This is all easiest to visualize if you draw a space-time diagram showing the paths of the two lance points and the two chests. Start by drawing it using coordinates in which the two warrriors are approaching each other from opposite directions at the same speed (call it $w$) and then transform into a frame in which one is at rest and the other is moving at some speed (which will not be $2w$, it will be $2w/(1+w^2)$ if we're measuring time in seconds and distance in light-seconds so that $c$ is equal to 1).

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Warrior M and S both have the exact same experience because of the symmetry of the situation - as far as each one is concerned they're at rest and the other one is approaching them at speed v. For both: The other guy's lance point smashes me in the chest. A moment later I see my lance point smashing the other guy in the chest, and somewhat after that I feel the butt end of my lance kick hard as the shock impact of the tip is transmitted down the shaft to my hand.
wait, got a question here, why would the warrior sees himself got stabbed first? isn't the opponent's lance shorter because of length contraction?

Nugatory
Mentor
wait, got a question here, why would the warrior sees himself got stabbed first? isn't the opponent's lance shorter because of length contraction?
It is, but it also takes some time for the light signal from the impact of my lance point on his chest to make it to my eyes so that I can see the impact. His lance point hits my chest while that light is still in flight.

Draw that space-time diagram!

It is, but it also takes some time for the light signal from the impact of my lance point on his chest to make it to my eyes so that I can see the impact. His lance point hits my chest while that light is still in flight.

Draw that space-time diagram!
OHH, I think I got the idea, thank you very much!!!

ghwellsjr
Gold Member
Let's assume in the symmetrical frame where both warriors are approaching each other that their speeds are 0.6c and that they have lances that are 5 feet long in their own rest frames. Since gamma at 0.6c is 1.25, this means their lances are Length Contracted to 4 feet in the symmetrical frame. In the following spacetime diagrams, I show the warrior on the left in blue with the tip of his lance in green and the warrior on the right in black with the tip of his lance in red:

As they approach each other, their tips pass at the Coordinate Time of 6.7 nanoseconds and then each tip simultaneously contacts the other warrior at the Coordinate Time of 10 nanoseconds. At this point we should consider each lance as a projectile because it will take a very long time for the shock waves to propagate through the lances and through the warriors and we would need more information to adequately show any more details on the diagram. Suffice it to say that the battle is a draw.

Now if we transform to the rest frame of the blue warrior, we see that his lance is 5 feet long while his opponent's is less than 2.5 feet long:

The tips pass at the Coordinate Time of 8.3 nsecs and a short time later at 11 nsecs, the blue warrior's lance contacts the black warrior. However, since the black warrior's lance is a projectile, its tip contacts the blue warrior 3 nsecs later and we see that it is again a draw.

We can transform to the rest frame of the black warrior and see that everything has flipped:

Now you can go to sleep.

ghwellsjr