nothing faster than light!

[firecracker]

Imagine a revolving light source somewhere on the surface of the earth. Instead of a lighthouse beam, let's make it a laser source. Let's locate a specific detector somewhere in space such that it can intercept the beam as it rotates. For simplicity, let's place it out there somewhere around1 million km so that the source doesnt have to rotate faster than, say, 1 RPM.
1. Can the beam swing faster (angular velocity) than 300,000 km/sec anywhere along its path?
2. If it does, can the beam be detected?

[snoopy]

Hi firecracker,

Im not sure if this is a serious question if the beam is only rotating at 1 revolution per minute how do you expect it to have an angular velocity in excess of the speed of light ?

Nothing can travel faster than the speed of light is the general consensus apart from some speculative ideas. There are a lot of good reasons for this
if your question is can anything travel faster than light then probably not 'relativity' gives you nonsense answers if you try and plug in veloctities above `c`. But some physicists and mathematicians have pointed out some `patterns` in theory could exceed the speed of light but its highly theoritical work. Nothing in nature has ever been detected going faster than light.

[Buffy]

This is actually an interesting question. Think about it snoopy: as the radius increases, the angular velocity does too. If your thinking were purely Newtonian, at some radius the angular velocity would reach and exceed c....

Hypothetically fast,
Buffy

[snoopy]

Errm not really sure im understanding you Buffy,

angular speed (omega) = 2*pi*f = v/r

where v = tangential velocity and r = radius of rotation
so if the radius increased the angular speed would decrease
to increase the speed the radius of rotation would have to be fractional and small.

But it is a bit of a non argument anyway as you cant use classical mechanics for things like light beams as you end up with crazy mixed up answers and you have to use quantum mechanics.

So could you explain what you mean or am I being dense ?

[Buffy]

We're using colloquial terms here (that's fair game on this site: we don't require people to be experts in order to discuss topics). In your equation, set v=c and solve for r...

A really long string,
Buffy

[snoopy]

Ahh so your saying Im being dense,

Thanks sigh....

Still not really getting why my tangential velocity is at c but ok I will stick around and play.... why not.
not much on TV anyway.

its still a bit like using K.E. = 1/2mv^2
and applying it to ions and because of their enormous speed then saying oh look I can power a small town out of a stream of ions (which you cant)

if your saying that individual particles inside the light beam could exceed the speed of light but bunch up and they even out as the speed of light maybe I could see where your coming from.

As it is im confused by what your saying but maybe you could explain it further how did my tangential velocity get so big and why am I using classical mechanics to describe the nature of light ?

[Buffy]

Its a problem where if one considers only classical mechanics that it would provide a mechanism for light to "exceed the speed of light."

The beam is revolving at 1 revolution per second. Your equation can be used to compute the tangential speed of a photon at one mile out which would be miles per second. Using simple classical mechanics one could extrapolate this out to say that a photon at a radius of greater than has an tangential velocity greater than the speed of light (300,000 km/sec).

The game is to tell why with Special Relativity that this is not the case!

Paradoxically fast,
Buffy

[Pyrotex]

Good job so far guys.
I think what Firecracker was getting at is an old problem in Relativity 1 class. Don't think of the photons in the light beam. Think of the spot of light that it projects against an imaginary "wall". You know, like teasing your cat with a pocket laser.

If the "wall" is far enough away, (Buffy showed just how far) then our spot of light would appear (to us) to travel along the wall at a speed faster than c.

This is just high school geometry. Now the hard question is, how come that spot of light is traveling faster than c, but we say that nothing can travel faster than c????

One answer is that a spot of light is not a "something". Not an object with mass, not material in any way. The photons that hit our eyes as we watch the "spot" are all traveling at c, just the way they should. There is NO object, thing, that is traveling faster than c, just an apparition. Voila!! Special Relativity not required.

Something like an optical delusion. Firecracker? Any questions?

[Janus]

To add to what Pyrotex has already said. Not only is nothing material traveling across the wall, neither is any type of information. IOW, you can't use this method to communicate between two points on the wall between which the spot passes.

[CraigD]

Originally Posted by firecracker

Can the beam swing faster (angular velocity) than 300,000 km/sec anywhere along its path?

“Swinging” a beam of light is not like swinging a pole.

The photons in a beam of light, from a LASER or other source travel from their source at the speed of light. Rotating the source of that light changes only the direction of the photons being emitted, not their speed, or the speed or direction of any photons that have already been emitted.

Originally Posted by Pyrotex

If the "wall" is far enough away, (Buffy showed just how far) then our spot of light would appear (to us) to travel along the wall at a speed faster than c.

This is just high school geometry. Now the hard question is, how come that spot of light is traveling faster than c, but we say that nothing can travel faster than c????

One answer is that a spot of light is not a "something". Not an object with mass, not material in any way.

I agree with that answer.

We can actually produce an effect like this fairly easily. A sufficiently powerful laser rotated at a mere 10 rotations/minute will paint a bright mark across the Moon’s surface that appears to move at never less than 1.3 times the speed of light. 3500 RPMs would allow a laser on a 100 m tall platform to paint a dot across a point on the ground from 11000 m to 10000 m away in about .0000024 s, for an apparent speed of about 1.34 c.

A string of light bulbs connected to precise timers can give the appearance of a moving point of light that exceeds the speed of light.

The appearance of motion is not the same thing as a moving object.