Can the intersection point of two light beams exceed the speed of light?

[lloydziegler]

TL;DR Summary

Can the intersection point of two light beams exceed the speed of light8

If two seperate, coherent light beams were to intersect at a slight angle near the viewer, and then very rapidly made parallel,could the intersection point move away from the viewer in excess of the speed of light? If so, could that intersection point be made visible somehow,and how would the Observer see it then?

 

[renormalize]

TL;DR Summary: Can the intersection point of two light beams exceed the speed of light8

Yes, see The Superluminal Scissors.

 

[Ibix]

Yes, see The Superluminal Scissors.

Careful - the scissor blades are moving perpendicular to the intersection point, and the laser light isn't, so I don't think these are strictly equivalent.

could the intersection point move away from the viewer in excess of the speed of light?

You can certainly make non-physical things "move" faster than light. I'm not sure you can do it with your setup, but the classic is to sweep a laser pointer spot across the face of the moon in a fraction of a second.

If so, could that intersection point be made visible somehow,and how would the Observer see it then?

Nothing special.

 

[lloydziegler]

So what is the explanation for sweeping a laser beam across the moon in a microsecond.... is it true that that laserdot moves faster than the speed of light?

 

[Ibix]

is it true that that laserdot moves faster than the speed of light?

Sure, but no physical object is exceeding the speed of light. Each bit of the light beam is doing $c$ in different directions, it's just illuminating different points. You could use a series of fixed lasers pointing in very slightly different directions and pulse them in sequence to achieve the same effect, if that makes what's going on more obvious.

And you can't use it to communicate faster than light - a guy on one side of the moon can't use this to contact someone on the other side because the beam isn't under his control, so there are no issues around causality here.

 

[DaveC426913]

Sweeping a laser across the Moon (or in a full circle across the heavens) is often analogized with a machine gun.

You can set a a machine gun on autofire and sweep it in a circle arbitrarily fast, so that the impact site of the bullets travels many times faster than the bullets themselves can travel. But you can also see why "the impact site of the bullets" is not a real thing that is moving - it is merely a semantic label for a series of discrete events.

 

[Mister T]

You can certainly make non-physical things "move" faster than light. I'm not sure you can do it with your setup, but the classic is to sweep a laser pointer spot across the face of the moon in a fraction of a second.

Well, if you can make one laser dot sweep across the surface of the moon at a speed faster than light, you can do it with two coinciding dots, which would be the intersection point of two laser beams!

 

[Ibix]

Well, if you can make one laser dot sweep across the surface of the moon at a speed faster than light, you can do it with two coinciding dots, which would be the intersection point of two laser beams!

Indeed. I think OP was imagining something slightly different, a pair of lasers counter rotating in a common plane until they become parallel. The intersection of those two don't move superliminally because the beams form spirals.

However, two non-rotating lasers making angles $\pm\theta$ to the $y$ axis and moving at constant speeds $\mp v$ along the $x$ axis produce beams that satisfy $\pm y\tan(\theta)=x\pm vt$ intersect at $y=vt/\tan(\theta)$ (or minus that if I messed up the signs...), which "moves" with speed $v/\tan(\theta)$, which may be made arbitrarily high for any non-zero $v$ by setting $\theta$ very small.

 

[PeroK]

So what is the explanation for sweeping a laser beam across the moon in a microsecond.... is it true that that laserdot moves faster than the speed of light?

These examples generally involve the illusion of motion. It involves something happening at point $X$ and a time $\Delta t$ later something happens at point $X + \Delta X$. We interpret this as motion, with speed $\Delta X/\Delta t$, but nothing has moved. It's just two separate events that give the impression of motion.

In the laser example, you could place an impenetrable wall in the "path" of the light across the moon and you could ask how the light passed straight through the solid wall? And, of course, the answer is that no light is actually moving in that direction. There is no motion across the face of the moon.

 

[Ibix]

illusion of motion.

A good way of putting it. And since it's not motion but an illusion of motion, it isn't restricted in the same way actual motion is.