What is the resolution to the lighthouse paradox?

[Zizy]

Well, let's assume you send out just one pulse of photons (light up just for a moment, then turn off again)... then let's assume you sent 10^20 photons out. Flash, when you are observing it close to the origin, appears bright. Further you go out, darker it gets. After a certain amount of distance, there will even be surfaces that won't be hit by photons at all... meaning you won't have circle anymore, but just some random spots hit by photons in a sea of darkness.

This could be extended to any number of photons with the same conclusion - unless there is some very good reason (and vacuum isnt, at least not for low energy photons), photons will travel straight (curvature of the space-time doesn't change this fact)

EDIT: This doesn't prove anything... it was just meant to say some things about speed of light and that the photons won't change their way only to keep the circle bright everywhere :)

 

[Dale]

The key is that the wet spot is not actually "made of water droplets," it is merely the location where the water droplets make contact with the wall. In the same way the "bright spot" from a lighthouse is not really made of photons, it is merely the location where those photons make contact with some object.

Well said.

I think the OP's "paradox" has been fully resolved multiple times now. If he wishes to continue his assertion I think he should post the wave equation that demonstrates superluminal velocity while satisfying Maxwell's equations. It can be done, but in the process of doing so he would learn the difference between phase and group velocity for a wave.

 

[DaveC426913]

Well said.

he should post the wave equation that demonstrates superluminal velocity while satisfying Maxwell's equations.

I would be satisified with a simple diagram - or even a good description - wherein he demonstrates photons moving at superluminal velocities. So far, nothing he's said hsows that to be the case. He jumps over a critical step in his description of the scenario.

 

[Tam Hunt]

I agree, the apparent paradox has been resolved and concede the point. However, in light of the previous discussions, I think the lighthouse paradox, with its circle of light, is not a valid predicate for the "motion of effects" arguments. If we imagine a variation of my original scenario, we can see why. Imagine a powerful light beam on a stationary platform in space (in relation to a distant planet). The light beam sweeps back and forth one arc second per second, with the distant planet at the center of its sweep. The distant planet, at one million light years distance, does not actually receive a circle of light at all. Rather, it just receives a few photons at best, due to the extreme attenuation that must happen at such distance. So there is not even a circle of light that is moving faster than light in this scenario. The only thing that could be said to be moving at superluminal velocity is an imaginary line representing the points the photons hit, as a previous poster pointed out.

Thanks for everyone's comments, this was quite helpful.

 

[JesseM]

I agree, the apparent paradox has been resolved and concede the point. However, in light of the previous discussions, I think the lighthouse paradox, with its circle of light, is not a valid predicate for the "motion of effects" arguments. If we imagine a variation of my original scenario, we can see why. Imagine a powerful light beam on a stationary platform in space (in relation to a distant planet). The light beam sweeps back and forth one arc second per second, with the distant planet at the center of its sweep. The distant planet, at one million light years distance, does not actually receive a circle of light at all. Rather, it just receives a few photons at best, due to the extreme attenuation that must happen at such distance. So there is not even a circle of light that is moving faster than light in this scenario. The only thing that could be said to be moving at superluminal velocity is an imaginary line representing the points the photons hit, as a previous poster pointed out.

That may be true if you're imagining a planet a million light years away, but you could just as easily imagine sweeping a powerful laser across the face of the moon--the spot would still be fairly confined when it reached the moon, and it could easily be made to move faster than the speed of light.