What is the resolution to the lighthouse paradox?

[Tam Hunt]

The classic lighthouse thought experiment leads to a situation in which some "thing" is traveling faster than the speed of light. This is the case because the lighthouse's light beam, if powerful enough, will shine a circle of light on its destination that can travel faster than the speed of light - as a function of the distance from the lighthouse itself.

The "motion of effects" argument is advanced to explain that the "thing," the circle of light, that is moving faster than the speed of light is not a real thing that contains any information. This is generally accepted as a way to avoid contradicting the relativity theory dictate that nothing can travel faster than the speed of light.

However, if we consider the lighthouse beam to be comprised of photons, as is of course the Standard Model's conception of light, we can see that the actual photons comprising the light beam can travel faster than the speed of light in a transverse direction. This is the case because the photons at, let's say, a million light-years from earth, may shift transversely much more quickly than their forward motion, as a function of the speed of rotation of the lighthouse itself. In this conception, it's not just an "effect" that is moving faster than the speed of light, but the photons themselves.

This thought experiment reveals, it seems, yet another paradox resulting from the Standard Model and relativity theory: if we accept that light is comprised of photons, then we must accept that they can indeed travel faster than the speed of light. But in this thought experiment, the photons may travel at a potential infinite transverse speed as a function of their distance from Earth.

Any thoughts?

 

[dkgolfer16]

However, if we consider the lighthouse beam to be comprised of photons,?

What else would it be comprised of?

can see that the actual photons comprising the light beam can travel faster than the speed of light in a transverse direction.

What makes you think this?

 

[ZikZak]

we can see that the actual photons comprising the light beam can travel faster than the speed of light in a transverse direction.

Um, no, the photons from a lighthouse don't have *ANY* transverse motion.

 

[Phrak]

"This is generally accepted as a way to avoid contradicting the relativity theory dictate that nothing can travel faster than the speed of light."

I take this to mean that relativity is wrong, but those clever but wrongheaded physicists have managed to find a loophole to slip through so they can keep their precious fantasy.

 

[LURCH]

Replace the lighthouse with a mounted machine gun. You may be firing the machine gun at one target (A), and then swing it 'round to fire at a second target (B). The bullets that were in flight on their way to target A do not suddenly leap sideways to strike target B. They continue traveling in a (fairly) straight line until they hit target A. Target B gets hit by bullets that were emitted from the muzzle of the gun after you swung it into its new position, in whatever amount of time it takes for those bullets to travel the distance from the muzzle to that target.

 

[Tam Hunt]

If we accept that the "motion of effects" circle of light can indeed move faster than the speed of light (as is the standard explanation), then we must also accept that the photons comprising the circle of light are moving faster than the speed of light in a transverse manner. If indeed the photons themselves are akin to bullets, then the circle of light will not move faster than the speed of light because the photons comprising the circle of light will not be able to get there fast enough to result in a circle of light moving faster than the speed of light.

As for what else the light beam may be comprised of, the Copenhagen Interpretation holds that light is actually a wave and a particle, depending on the situation. The generally accepted interpretation of the nature of light traveling through empty space is that it is comprised of particles. There are other, non-mainstream theories, that hold light is not comprised of particles.

 

[Phrak]

If we accept that the "motion of effects" circle of light can indeed move faster than the speed of light (as is the standard explanation), then we must also accept that the photons comprising the circle of light are moving faster than the speed of light in a transverse manner. If indeed the photons themselves are akin to bullets, then the circle of light will not move.

Uh, no, indeed we are not compelled.

If indeed the photons themselves are akin to bullets, then the circle of light will not move.

Indeed, if the photons themselves are akin to bullets, then the circle of light will move.

 

[Fredrik]

As for what else the light beam may be comprised of, the Copenhagen Interpretation holds that light is actually a wave and a particle, depending on the situation.

Particles in quantum mechanics behave that way, but there's no need to bring quantum mechanics into this. For the purposes of this discussion, we can think of light as consisting of massless classical point particles. I will still call them photons here since there's no word for "massless classical point particle".

If we accept that the "motion of effects" circle of light can indeed move faster than the speed of light (as is the standard explanation), then we must also accept that the photons comprising the circle of light are moving faster than the speed of light in a transverse manner.

Not at all. There is no transverse motion at all. Imagine a circular wall around the lighthouse (a very big circle). The photons are moving in straight lines from the lighthouse to the wall. (How could they do anything else? There's nothing in the space between the lighthouse and the wall that can make them accelerate sideways). When they hit the wall, they are scattered in every direction. If some of them hit you directly in the eyes, then you will see a dot.

Nothing is really moving faster than c in this scenario. The coordinates of the location on the wall that's being hit by photons at time t are changing with time faster than c, but that obviously doesn't violate relativity in any way.

 

[Tam Hunt]

There is no transverse motion at all. Imagine a circular wall around the lighthouse (a very big circle). The photons are moving in straight lines from the lighthouse to the wall. (How could they do anything else? There's nothing in the space between the lighthouse and the wall that can make them accelerate sideways).

Fredrik, imagine a very large circle defined by a light beam emanating directly upwards from Earth, at a million light years from Earth. This circle will have circumference pi*2 million light years. During the time Earth rotates one hour, the light beam will move, at the limit of the circle described, (pi*2 million ly)/24. If this is the case, the end of the light beam will be moving far faster than the speed of light. But how does that beam get over that distance in just one hour? There are in fact photons traveling that distance, under the current theory. But for photons to be striking a spot (let's say a distant planet's surface) 1 million ly from here, an hour after the beam of light was striking a different spot many light years away, we see that there must be transverse motion of the photons. This is the case because there were no photons traveling that straight line route through space until the beam rotated with the rotation of Earth. And now, an hour later, there are photons traveling that straight line route. Yet photons can't move faster than the speed of light. Hence the paradox.

Accordingly, it seems that either the particle theory of light is wrong or the prohibition against exceeding the speed of light is wrong.

 

[DaveC426913]

There is no paradox.


Let's simplify this.

The lighthouse fires 2 photons (it's a very dim lighthouse beacon). The targets are 180 degrees apart and each one light year distant from Earth.

The lighthouse spins at 60RPM (1R/s), firing one photon at the west target, then one photon at the east target .5 seconds later.

The two photons hit their opposing targets a year later, but only .5 seconds apart.

Our (very small, very dim) circle of light has swept out an arc that is one light year in radius and pi light years long. In .5 seconds. Our circle of light has moved 3+ light years in .5 seconds, well above the speed of light.

Now, which photons exactly, have exceeded c??

Part II: Add a third photon into the mix, at the .25s mark and therefore heads off North. Continue brighten the beam by adding photons fired at regular intervals (and resulting intermediate angles) until you are convinced you have a full and continuous beam of light from your lighthouse.

No photons have exceeded c.



Alternately, reexamine the machine gun analogy; you will see the error of your ways. It is quite easy to sweep a hail of bullets around where the transverse speed of "the hail of bullets" exceeds the velocity of the bullets themselves. No bullets have made any transverse motion; no bullets have exceeded muzzle velocity.

 

[ZikZak]

an hour after the beam of light was striking a different spot many light years away, we see that there must be transverse motion of the photons.

No, the photons striking the first spot were always aimed at the first spot since the moment they left the Earth. The photons that then strike the second spot were always aimed at the second spot since the moment they left the Earth. THERE IS NO TRANSVERSE MOTION OF ANY PHOTON. The "beam" of light is not a rigid meter stick, sticking out of the lighthouse, as you seem to be assuming.

Accordingly, it seems that either the particle theory of light is wrong or the prohibition against exceeding the speed of light is wrong.

I can think of another possibility.

 

[DaveC426913]

Here is the machine gun / light beam effect graphically.

http://www.davesbrain.ca/miscpix/machine gun effect.swf
Not only does no photon move faster than c, but we can see that no photon has any transverse motion; they follow perfectly straight, radiating trajectories from machine gun/lighthouse to target.

 

[ZikZak]

Here is the machine gun / light beam effect graphically.

Nice!

 

[paw]

Here is the machine gun / light beam effect graphically.

http://www.davesbrain.ca/miscpix/machine gun effect.swf

Very nice. The animation is particularly well suited to this problem.

 

[Fredrik]

Fredrik, imagine a very large circle defined by a light beam emanating directly upwards from Earth, at a million light years from Earth. This circle will have circumference pi*2 million light years. During the time Earth rotates one hour, the light beam will move, at the limit of the circle described, (pi*2 million ly)/24. If this is the case, the end of the light beam will be moving far faster than the speed of light. But how does that beam get over that distance in just one hour? There are in fact photons traveling that distance, under the current theory.

That's not true. The photons are moving in straight lines from the lighthouse to the target.

Also, do you realize that if they didn't, something would have to accelerate them in the "sideways" direction?

But for photons to be striking a spot (let's say a distant planet's surface) 1 million ly from here, an hour after the beam of light was striking a different spot many light years away, we see that there must be transverse motion of the photons.

No. The two spots were just hit by different photons.

This is the case because there were no photons traveling that straight line route through space until the beam rotated with the rotation of Earth. And now, an hour later, there are photons traveling that straight line route. Yet photons can't move faster than the speed of light. Hence the paradox.

You're not making sense here.

Accordingly, it seems that either the particle theory of light is wrong or the prohibition against exceeding the speed of light is wrong.

...or...you are.

 

[Tam Hunt]

DaveC,

Your simplification goes a bit too far because the motion of effects is not observed with single photons, but only with groups of photons. There is no "circle of light" with only one photon. There is only one photon. I agree with your thought experiment regarding only one photon.

But when we have a beam of light consisting of many many photons, we realize the difficulty of the photon conception of light vis a vis the prohibition of faster than light travel.

The beam of light in my hypothetical (shooting straight up from the surface of Earth) would in fact proceed forward at the speed of light, forming a spiral as it proceeds due to the radial motion of Earth. Accordingly, by the time it reaches my hypothesized planet 1 million lys away, we have a very large spiral of light forming a very spread out ellipse on the surface of the distant planet. I agree that there's nothing to "yank" the photons transversely at greater than the speed of light. Yet the standard argument is that indeed this is a situation in which the "motion of effects" can lead to some "thing" (in this case, not a real thing, but an artifact) moving faster than c.

My point in this hypothetical is that if there is indeed a circle of light (or actually an elongated ellipse) that is moving faster than c, that that circle is comprised of photons that must move faster than c. Again, hence the paradox.

 

[atyy]

The real question should be: can faster any known faster than light effects be used to communicate meaningful messages faster than light?

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html
http://www.physicsguy.com/ftl/

 

[Doc Al]

My point in this hypothetical is that if there is indeed a circle of light (or actually an elongated ellipse) that is moving faster than c, that that circle is comprised of photons that must move faster than c.

Still wrong. Your "circle of light" doesn't move faster than c, just the intersection of it and some surface does. But this has no special meaning. Certainly the photons comprising the circle are not moving faster than c.

Again, hence the paradox.

Only in your mind.

Check out the first link that atyy provided.

 

[DaveC426913]

Your simplification goes a bit too far because the motion of effects is not observed with single photons, but only with groups of photons. There is no "circle of light" with only one photon. There is only one photon. I agree with your thought experiment regarding only one photon.

I thought you might say this but I was hoping you would extrapolate the demo before responding. Add more photons into the demo. Add as many as you want. Add trillions. Add them until the cows come home. You will see that the demo is indeed valid model.

Please be specific about where you see the demo breaking down.

Yet the standard argument is that indeed this is a situation in which the "motion of effects" can lead to some "thing" (in this case, not a real thing, but an artifact) moving faster than c.

This is a good point that I was going to bring up. There is nothing moving faster than c. There is no "thing" (such as a spot of light) at all.

It's not even virtual as you say, it's nothing more than a semantic definition by a human.

There is light impinging on a surface here. And there is light impinging on a surface there. And then again over there. But the photons in all these places are not related. They do not belong to any club called "beam of light", nor does the lit area of the planet here have any relationship at all to the lit area of the planet over there.

The only way these areas of light have anything to do with each other is in our imaginations - a sort of conceptual persistence of vision thing, if you will.

And, being that it is only in our minds that two spots of light are to be considered the same "thing", it is no more valid than any other conceptualization of our minds, such as "I imagine I am here on Earth, and now I imagine I am on Jupiter". Conceptually, I've just flown half a billion miles in one second.

My point in this hypothetical is that if there is indeed a circle of light (or actually an elongated ellipse) that is moving faster than c, that that circle is comprised of photons that must move faster than c. Again, hence the paradox.

You still haven't shown how that is true. And it has been demonstrated to be false. Stating it again doesn't make it more true. The paradox is only in your conceptualization.

I think we've all been pretty generous in modeling how it works without any paradox. If you want to continue, I'm afraid you're going to have to be a little more forthcoming with your own model showing this paradox.

 

[Tam Hunt]

Doc, what is the circle of light comprised of? In the standard model, it's comprised of photons. Accordingly, if the circle of light is moving faster than the speed of light, the photons themselves are necessarily moving faster than the speed of light in the thought experiment I've outlined (with a perimeter at 1 million lys from Earth).

I'm urging you to take a step back and think about the "motion of effects" arguments offered to explain why the faster than c prohibition is not actually broken. The standard motion of effects argument doesn't consider the fact that for there to BE a circle of light, there have to be photons comprising that circle of light.

Either the photons are breaking c, or the circle of light itself doesn't move faster than the speed of light. With the spiral I wrote of in my last post emanating from Earth as the light beam rotates, the better explanation may be that the circle of light doesn't actually move faster than the speed of light. Rather, it moves at the speed of light, as the rotating spiral spreads outward at the speed of light.

 

[ZikZak]

Doc, what is the circle of light comprised of? In the standard model, it's comprised of photons.

But not the same photons. The initial "circle of light" is not made out of the same photons that make up the final "circle of light" after it has moved. They are made of different sets of photons that have nothing to do with each other. Each set of photons is traveling radially outward from Earth, and has never had any transverse motion whatsoever.

*bangs head against wall*

 

[DaveC426913]

Doc, what is the circle of light comprised of?In the standard model, it's comprised of photons.

No it is not.

This "circle of light" is an entirely human fabrication. It thinks this pattern of light impinging on this part of a planet is "the same" as that pattern of light impinging on that part of the planet. It is we humans who make the mistake of thinking that it is "a" thing at all - as opposed to the way it really is: uncountable photons traveling from lighthouse to target, alone and oblivious to each other.


The animation provided is the way it works. Nothing you've said has changed that.

 

[Doc Al]

Doc, what is the circle of light comprised of? In the standard model, it's comprised of photons.

OK.

Accordingly, if the circle of light is moving faster than the speed of light...

It's not. Next?

If the "circle of light" is composed of photons, how could it be moving faster than the speed of light?

Either the photons are breaking c, or the circle of light itself doesn't move faster than the speed of light.

I agree with that.

 

[Doc Al]

Here's yet another example of how you can get an imaginary point moving faster than the speed of light that has nothing to do with photons. Have one thousand (or a million) people stand in a line, each holding a ball. Let the line of people be as long as you want, say 1 mile long. Now have each of them drop their ball in turn: First person 1, then person 2, etc., with each person waiting 1 trillionth of a second to drop their ball (compared to the last person). So, you'll soon have a line of balls falling to the ground. I hope you'll agree that the balls never reach anywhere near the speed of light. The intersection of that line with the ground (as the balls hit the ground) will travel 1 mile in a billionth of a second--or 1 billion miles per second. That's quite a bit faster than light speed, yet nothing really traveled anywhere close to the speed of light. No mystery, no paradox.

 

[Tam Hunt]

Doc, I agree with your example as a theoretical motion of effects situation exceeding the speed of light. But it seems the motion of effects argument vis a vis the lighthouse paradox (that I've embellished a bit in the above posts) breaks down because the circle of light itself is comprised of photons. It's not "just" a conceptual thing as DaveC argues. For there to be light, there has to be photons under the Standard Model. Accordingly, the circle of light, while an abstraction in terms of the circle itself, to be sure, is still comprised of photons insofar as there is illumination. I think the better analysis is that neither the circle of light nor the photons move faster than the speed of light.

 

[Doc Al]

Doc, I agree with your example as a theoretical motion of effects situation exceeding the speed of light. But it seems the motion of effects argument vis a vis the lighthouse paradox (that I've embellished a bit in the above posts) breaks down because the circle of light itself is comprised of photons. It's not "just" a conceptual thing as DaveC argues. For there to be light, there has to be photons under the Standard Model. Accordingly, the circle of light, while an abstraction in terms of the circle itself, to be sure, is still comprised of photons insofar as there is illumination.

You can still get "faster than light" effects using a sweeping beam (or circle) of photons, but it has no more significance than the faster than light effects that I demonstrated with the falling balls. No "thing" is moving faster than light; no faster than light signaling takes place.

I think the better analysis is that neither the circle of light nor the photons move faster than the speed of light.

If by "circle of light" you just mean the expanding circle of photons, then of course they don't move faster than light.

But you can certainly use it to create a moving "spot" that appears to travel faster than light. So what?

 

[JesseM]

Doc, I agree with your example as a theoretical motion of effects situation exceeding the speed of light. But it seems the motion of effects argument vis a vis the lighthouse paradox (that I've embellished a bit in the above posts) breaks down because the circle of light itself is comprised of photons. It's not "just" a conceptual thing as DaveC argues. For there to be light, there has to be photons under the Standard Model. Accordingly, the circle of light, while an abstraction in terms of the circle itself, to be sure, is still comprised of photons insofar as there is illumination. I think the better analysis is that neither the circle of light nor the photons move faster than the speed of light.

The distinction Doc Al made at the end of his last post is a good one. When you talk about the "circle of light" are you talking about spot made by the beam on a circular wall with the lighthouse at the center (in which case the spot can move faster than light, but the photons making up the spot at one moment are different than the photons making up the spot at a later moment, so no individual photon needs to move faster than light), or are you talking about the spiral of photons moving away from the lighthouse as viewed from above (in which every photon making up the spiral is moving at the speed of light in a purely radial direction away from the lighthouse)?

 

[Helios]

JesseM at last mentions the word spiral. I would think the stream of photons would form Archimedean spirals. We know that the solar wind is emitted radially from the surface of a rotating sun and that these streamlines actually do form Archimedean spirals. This is the so-called garden-hose effect.

 

[DaveC426913]

If by "circle of light" you just mean the expanding circle of photons, then of course they don't move faster than light.

I have asked and asked for a more detailed description of what he's talking about and he won't cough it up. Your suggestion is the kind of thing he might be talking about but, unless he embellishes his scenario to eradicate possible misunderstadnings, we're just talking in circles.

Tam. Please describe in detail the setup you are talking about. Most of us are picturing a spot of light sweeping across a target, as if you waved a flashlight back and forth; the beam forms a disc of light that moves back and forth. If this is not what you're envisioning then please illuminate us.

 

[LURCH]

... This is the so-called garden-hose effect.

Funny you should mention hoses; here is another analogy, very similar to the machine gun illustration, but with a difference that might be important.

Suppose you have a very high-pressure hose, like the nozzle on a fire engine. Water exits the nozzle at such great velocity that it can travel 100 yards to strike a distant wall. This velocity would still be well below the speed of sound. So, you stand at the center of a large circular stadium spraying water and a wall 100 yards away. You could say that the wet spot, or "splash," on the wall is made of water droplets. This would be exactly the same as saying that the circle, or ellipse, of light is made of photons. Keeping the hose at a constant elevation, you suddenly turn around and begin spraying in the opposite direction. This could be done in one third of the second. Of course, water droplets that left the hose before you started turning would be unaffected, and travel along their (somewhat) straight path to hit the wall exactly where all previous drops have hit. But, there would be a moment when the "wet spot" on the wall is in its original location, and then, one third of a second later, the wet spot is in a new location 200 yards away from the original.

Did any water droplets travel 200 yards in one third of a second? The "wet spot" or "splash" has exceeded Mach 1, so where's the sonic boom?

Replace the water droplets with photons, and the wet spot with the bright spot, and the situation is exactly the same. 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. When the lighthouse sweeps its beam, the photons do not exceed the speed of light any more than the water droplets from the hose exceed the speed of sound.

 

[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.