Lighthouse paradox revisited

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

What else would it be comprised of?

What makes you think this?

ZikZak

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 travelling in a (fairly) straight line untill 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

Uh, no, indeed we are not compelled.

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

Fredrik

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".

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

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

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.


I can think of another possibility.

DaveC426913

Here is the machine gun / light beam effect graphically.

http://www.davesbrain.ca/miscpix/mac...n%20effect.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

Nice!

paw

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

Fredrik

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?

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

You're not making sense here.

...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/physic...Light/FTL.html
http://www.physicsguy.com/ftl/