The thing to note about the scissors is that the parts of the blade that intersect must’ve started to move before they intersect, so the speed of the intersection is not the speed of sound in the blades as the intersection is always behind the intial sound wave. However the speed of the intersection is no necessarily constant and it can start off slowly and ‘accelerate’ to arbitarily high speeds.
Thor could do it. With a hammer, I mean. It wouldn’t even have to be HIS hammer, though Mjolnir would be easiest. I’m not sure what he could accomplish with scissors but I am confident that Athena could find a way if Jord’s son could not.
Btw in passing, there is a concept of rigidity in special relativity, known as ‘Born rigidity’, this not exactly the same as the Newtonian idea of rigidity as the shape (in a given reference frame) of an a Born rigid object may deform due to length contraction. Also there are actually quite severe constraints on how a Born rigid object may move and remain Born rigid.
Of course the speed of sound in a Born rigid object would technically be infinite as in a Newtonian rigid object, but this can be got around by simply saying that forces are applied throughout the body in such a way to maintain Born rigidity.
Okay, I’m starting to see your point… but …
Try this: You see the force starting at the handles of the scissors, propagating towards the joint, then passing the joint towards the blades, along a wave that can’t possibly go faster than light.
But what if the force is applied to the blade?
If you concede that my triangle would work, then consider a similarly-built scissors. The blades are twelve inches long, they currently cross each other two inches from the joint, and are ten inches long beyond that. The two tips are one inch apart. In the middle of the blade, and right at the blade’s edge, I apply a force, making that point on the blade move toward the other blade at one-fifth of the speed of light. This force propagates toward the joint and toward the tip at a rate of – oh, for the sake of argument, half the speed of light, which is still too slow for any significant dilation effects.
Let’s see what happens one arbitrary unit of time later - let’s call it a “sekond”: The point at which I applied the force has moved 0.2 light-sekonds toward the other blade. The wave has propagated 0.5 light-sekonds towards the joint and towards the end.
It is now one sekond after the force was applied. The propagation wave has reached two points, one light-sekond apart from each other. Let’s call those points A and B.
Another second elapses. Point A is moving toward the other blade at 0.2 of c, and Point B is also moving toward the blade at 0.2 c. Let’s say that Point A has just now made contact with the other blade. But Point B is farther from the joint, and hasn’t met it yet.
Let’s see… it took 2 sekonds for Point A to touch the other blade. Point B is 1 light-sekond further away. I defined my triangle to have a 10% angle, so it must be that it will take Point B a total of 2.2 sekonds to touch its spot on the other blade.
If that’s so, then Point B will touch the other blade only 0.2 sekonds after Point A did. But they are a full light-sekond away from each other along the blade. It seems to me that the point where the blades touch moved at 5 times the speed of light.
Where’s my error?
Your error is in trying to close the scissors too rapidly. Do it again, slowly enough that the waves have a chance to propagate out to the ends before the near parts start coming together.
I am no physicist, but I think part of your error is failing to realize that you the force you apply to your system is NOT and cannot be applied instantaneously. I know it SEEMS to be applied instantaneously when you try it with a real pair of scissors, but that’s because the distances are so small compared to speed of the force.
When someone enters the room and starts speaking to me simultaneously, the sound of his voice appears to arrive at the same time as the light reflected from his body. But that’s because he’s only a few feet away, and so the time it takes the sound to reach me is not perceptible to human senses. But make the distance far enough, and I can see that light travels far, far faster than sound.
Similarly, the force applied to the scissors does not have effect in zero time. The maximum speed at which that force can travel is going to be less than the speed of light.
Who cares when the waves finally reach the ends? I did wait one sekond for the waves to reach a point 0.5 light-sekonds on each side of the point where the force was applied. And I’m labeling those points as A and B, and they both start moving at the same time.
Okay, I do think I made some minor arithmetic errors, which I’ll now correct.
Over the course of one sekond (from the beginning of second #2 until the end of sekond #2) Point A began moving and then reached the other side.
Point B began moving at the same time as point A (because it is equidistant from the point where the force was applied).
But because of the 10% angle, it will take 10% longer for Point B to reach the other side. Thus, Point B will reach the other side when it has been traveling for 1.1 sekonds, which is 2.1 sekonds after the force was applied, i.e., soon after the third sekond has started.
So: Point A got to the other side 2.0 sekonds after the force was applied. Point B got to the other side 2.1 sekonds after the force was applied. And the point of intersection moved 1.0 light-sekonds in only 0.1 sekonds – ten times the speed of light.
When you first start moving the handles, the blades will be all wiggly, as the waves from the handle movement propagate out along the blades. If you move them slowly, though, those waves will have a chance to settle down before they go too far, and the blades will end up moving uniformly.
Huh?
Thank you!
Even with this very clear explanation, I found it surprisingly hard to visualize or to decide what could legitimately be inferred, but after some thought I am almost completely certain that you are absolutely correct.
I should hastily add:
The point of intersection is not an object - it’s just a concept, so nothing is moving faster than light in any scissors scenario. Concepts can appear to move at any speed by simply re-describing them; there’s a penguin here- now the penguin is on Jupiter - the conceptual penguin moved faster that the speed of light; the scissors are intersecting here - now they’re intersecting there - but the intersection.itself is just an idea - the physical material of the blades themselves is not doing anything extraordinary - it can’t.
You are missing an important point -Relativity 101:
As relative speed increases, 3 things apparently happen
- mass increases
- distance decreases (along the direction of motion)
- time slows
As you start to swing the hammer with the mythical rigid handle faster and faster, the energy needed to accelerate it to a faster speed also gets larger. To reach the speed of light takes infinite energy - you cannot do it.
For example what is the value of y in y=1/x at x=0? Consider x=0.1 then 0.001 then 0.00001 and so on. All indications are that at zero, y is infinite. Same when you consider approaching the speed of light. The energy required is asymptotic, infinite.