Scissor Blade Problem

[Pikkugnome]

TL;DR

A common scissor blade problem stemming from special theory of relativity.

This is a common exercise stemming from special theory of relativity courses all over the world it seems. Show that the intersection of scissor blades can move faster than the light. If we imagine that we put a pen in between the scissors, touching the blades, and it is sliding without much friction, then the intersection point of the blades is at a certain distance from the pen. If the blades are pushed together, the pen slides forwards. However due to geometry of the situation, the point of intersection lags further behind from the pen. Therefore it is moving slower than the pen, thus less than the speed of light, since the pen can't move faster than the light.

 

[Ibix]

Yes. The intersection point can move faster than light, but it does not have to. You've added a constraint that forces it not to.

 

[pbuk]

Show that the intersection of scissor blades can move faster than the light.

In order to do this you must be able to close the scissors very quickly.

If we imagine that we put a pen in between the scissors, touching the blades, and it is sliding without much friction

Do you think you will still be able to close the scissors quickly enough? Apart from friction, what do you think could prevent this?

 

[PeroK]

TL;DR Summary: A common scissor blade problem stemming from special theory of relativity.

This is a common exercise stemming from special theory of relativity courses all over the world it seems. Show that the intersection of scissor blades can move faster than the light. If we imagine that we put a pen in between the scissors, touching the blades, and it is sliding without much friction, then the intersection point of the blades is at a certain distance from the pen. If the blades are pushed together, the pen slides forwards. However due to geometry of the situation, the point of intersection lags further behind from the pen. Therefore it is moving slower than the pen, thus less than the speed of light, since the pen can't move faster than the light.

If you have a guillotine, rathen than scissors, then all points on the blades hit the surface simultaneously. If you consider the "motion" of the point of intersection in that case, then the speed is infinite. Or, perhaps better, you have a tiny angle on the blade and the speed is "almost infinite".

 

[Pikkugnome]

I add a little. The constraint is very loose, just an imaginary disc moving slower than the speed of light in between the blades, which seems to prevent the point of intersection moving faster than the light. It is not easy to find physical assumptions, which would be more forgiving.

I add that why not pull the blades, and since the pen is now moving inwards, towards the jaw, so the point of intersection is moving faster than the pen. I don't think you expected this slick move. Unfortunately you can imagine another pen the opposide side in between the handles, it will doing the opposite movement away from another point of intersection and presumably slower than the speed of light. What happens next I leave to you.

I urge you not to give this example for your students and not be prepared for this argument.

 

[Ibix]

Um... I repeat what I said above. The intersection point can exceed the speed of light. It doesn't have to.

The main reason people set this kind of example is to understand why it's possible for the intersection to exceed light speed. Finding circumstances where it doesn't is amusing, but it's also missing the important learning point.

 

[Pikkugnome]

I just wanted to highlight the geometric side of the problem. It is not as clean as it should. Maybe my reasoning is false even from geometric point of view. The problem is easy to model as plane geometry, but I have never done it, I have just used the pen in between the blades argument.

 

[Ibix]

Maybe my reasoning is false even from geometric point of view.

I don't think your reasoning is false, I just don't see the point. You've taken a scenario that is supposed to demonstrate one thing (some "things" can "travel" faster than light because they are neither physical things nor actually travelling) and added a feature that stops it demonstrating that. There's nothing wrong with the physics of that, it's just hard to see the point.

 

[Pikkugnome]

The part I talk about pulling the blades to the opposite direction is false and what ever followed as well.