Is a Rapidly Rotating Searchlight a Violation of Special Relativity?

[Barry Melby]

Homework Statement

Consider a searchlight on the ground that casts a spot on a cloud 1500 m overhead. If the searchlight is rotated rapidly−say, 40 ∘ in 1 μs−—how fast does the spot move in the Earth reference frame when the searchlight is directed vertically upward?

I have solved this part and found the velocity to by 3.5c.

Is this a violation of special relativity?
1. No, this is not a violation of the special relativity, light spot is not a physical object and can move with any speed.
2. Yes, this is a violation of the special relativity, the searchlight cannot really rotate this fast, data given in the problem statement is incorrect.
3. Yes, this is a violation of the special relativity, this situation should be studied using general relativity.

Homework Equations

The Attempt at a Solution

I think it is a violation, but I'm not sure exactly the reasoning behind it. My educated guess would be number 2 is the correct answer.

 

[phinds]

No, there isn't anything that is actually moving except the rotating search light. This canard is regularly debunked here on PF. No 1 is correct.

 

[Ray Vickson]

Homework Statement

Consider a searchlight on the ground that casts a spot on a cloud 1500 m overhead. If the searchlight is rotated rapidly−say, 40 ∘ in 1 μs−—how fast does the spot move in the Earth reference frame when the searchlight is directed vertically upward?

I have solved this part and found the velocity to by 3.5c.

Is this a violation of special relativity?
1. No, this is not a violation of the special relativity, light spot is not a physical object and can move with any speed.
2. Yes, this is a violation of the special relativity, the searchlight cannot really rotate this fast, data given in the problem statement is incorrect.
3. Yes, this is a violation of the special relativity, this situation should be studied using general relativity.

Homework Equations

The Attempt at a Solution

I think it is a violation, but I'm not sure exactly the reasoning behind it. My educated guess would be number 2 is the correct answer.

Suppose you replaced the searchlight by a laser and the distance 1500m by the distance to the moon. You could rotate a real laser at a not-excessively fast rate entirely within practical bounds, and make the light-spot on the moon's surface move much faster than c. So, (2) is not really relevant, although it might be for a big, heavy searchlight---that's why I suggested a laser. That is, moving an actual searchlight through 40° in 1 μsec might be impractical, but you can easily wave a laser by hand with no trouble.

That leaves (1) or (3).

 

[phinds]

[post deleted]

EDIT: OOPS. I thought I was responding to the OP. Sorry Ray.