Faster then light..-ve index...

[CPL.Luke]

no it wouldn't

 

but that still doesn't change the fact that that is what happens in a meterial with a negative index of refraction.

[rajama]

I remember reading about this back in 2000: the pulse is very long and I think carefully crafted to have a stable symmetrical shape.

 

It’s interesting, as the first thing people pointed out about earlier experiments was that the shape of the pulse distorted, the peak skewing forward (moving toward the front edge) as it propagated - and here they tried to suppress that feature…

 

The speed measurement was entirely related to the passing of pulse peak… I assume this shape distortion still occurred but that the pulse length made the skew, and the pulses leading edge, unobservable.

 

Trying to get a handle on what happens, don’t think of this ‘pulse’ is a simple object. Neither is it’s ‘movement’ through a medium who’s atoms have already been energised by a laser; although there is no net energy transfer from the medium to the pulse, the medium ‘supports’ the pulse... and allows it to move far more rapidly than in normal space.

 

As the group velocity of a pulse is always associated with information transfer this seemed like a superluminal transport of information, but what you have is a pre-existing object impinging on another, like a searchlight scanning a wall.

 

Hopefully this makes some sense and isn’t too far wrong.

[5614]

Okay' date=' since I was challenged to think about it, I did. Here is what I came up with:

If you take your laser pointer, shine it on your ceiling and turn it so fast that the dot should be moving faster than the speed of light, you would see something quite weird. The dot will first appear on the ceiling almost directly above your head, then it will split and become two dots and going in opposite directions.

Would you take my word for it? I didn't think so! [/quote']What the. We are talking about a normal ceiling here, not some negative index one.

 

OK, imagine you are holding the laser vertically upwards. You are rotating the laser about some point in the middle of the laser unit. Imagine you rotate it 1°. Imagine there is 0.25m between the center of rotation and the top of the laser. Imagine there is 10m between the center of rotation and the ceiling.

 

Now the top of the laser unit moves [math]\frac{1}{360} \times 2 \times \pi \times 0.25 = 0.004[/math] meters.

 

However the top is different. Firstly we are dealing the distance the dot moves on a horizontal surface. So we use trigonometry, as we want to find the opposite or the distance the dot moves across the ceiling when the laser unit is rotated through 1°. Remembering there are 10m between the center of rotation and the ceiling the distance the laser dot moves is: 10tan(1) = 0.175m.

 

This use of trig in this problem only works up to (but not including) 90°, because at that point the laser beam travels parallel to the ceiling and so never actually collides with it.

 

Right, so that's the theory. The edge of the laser unit moved 0.004m whereas the the laser dot moved 0.175m in the same period of time.

 

Now I'm going to rearrange the numbers to show the dot moving faster than the speed of light.

 

OK, here are the new numbers:

>> Rotation through 85°

>> Center of rotation to top of laser unit is still 0.25m

>> Center of rotation to ceiling 10,000m (or 10km - now I know that is quite high, so we're probably talking about the sky and a very high cloud!)

 

OK; so the laser dot moves [math]10,000 \times tan(85) = 114,301[/math] meters.

 

So for the dot to travel faster than c (300,000,000) we need the time taken to be [math]\frac{distance}{speed} = \frac{114,301}{300,000,100} = 0.000381[/math] seconds.

 

Note how I gave speed as 300,000,100 so that rotating the laser unit 85° in the calculated time gives a speed >c.

 

Now to ensure this is actually possible we have to check the speed at which the laser unit rotates, because that cannot move faster than c.

 

So the top of the laser unit will move a distance of [math]\frac{85}{360} \times 2 \times \pi \times 0.25 = 0.371[/math] meters.

 

Therefore in time t=0.000381 the fastest moving part of the laser (the top) will move at 0.371/0.000381 = 973m/s which is fine.

 

So we have the laser rotating at 973m/s and the top moving at 300,000,100m/s which is >c.

 

Understand now?

[Mowgli]

So we have the laser rotating at 973m/s and the top moving at 300' date='000,100m/s which is >c.

 

Understand now?[/quote']

 

Are you sure about this?

 

You are thinking of the laser as though it were a solid rod, so that if you rotated the laser, the dot (10km away) would move instantly. It wouldn't. It would take 10km/c before the dot moved. (You point the laser in a new direction, then the laser has to reach the ceiling from the new position.) If you worked out the equation for the position of the dot as a function of time, you would get a fourth order equation with two admissible solutions for any given time. I know you still don't believe me, but I hope to convince you tomorrow. It is too late where I'm right now.

 

BTW, the dot (at least one of the two) does move faster than c, but only for a very short time.

[CPL.Luke]

5614 is right, once the dot starts moving the dot will move faster than c (as long as the laser instantly started rotating at 85 degrees per the unit time that 5614 gave before)

 

you can treat the laser as a bar and get the same general result as if you did the problem while taking into account the travel time between the laser and the wall.

 

 

if anybody has the abiity to create an animation out of the polar equation

 

[MATH] \theta =\omega t[/MATH]

 

and

 

R=Ct

 

it would show how the dot moves quite well, but if nobody has the ability to do that someone could post the graph of R=C/omega t which should show the spiral that a light pulse would follow as it left the laser.

[Mowgli]

if anybody has the ability to create an animation...

You stole my thunder! An animation was precisely what I was going to spring on 5614 today.

 

 

In the animation above, the laser pointer is at the bottom-center of the figure. I'm turning it so fast that the laser dot on the ceiling should travel at 10c (which is indicated by the white circle moving across the ceiling.) But it takes a while for the laser to reach the ceiling. The light is indicated by the small red dots which move towards the ceiling (10 times slower than the white circle). The dot appears when the light hits the ceiling.

 

As you can see, the light from the laser first hits the ceiling at a point close to the top (indicated by the black dot), and subsequently, light on either side starts hitting the ceiling, making two dots (in yellow and green). This is the how one laser pointer creates two dots appears at two places at the same time. Note how the dots slow down considerably as they move away from the center. Light travel time effects dominate at shallow angles.

 

But CPL.Luke is right. If the ceiling was a spherical shell and the laser was at its center, there would be only one dot moving at 10c. (At least, that's what I get when I try to work it out.) In effect, by having a spherical ceiling, you are cutting out the shallow angles; the laser is always perpendicular to the ceiling. In this case you can treat the laser as a solid rod, but with a constant delay equal to r/c (which differentiates to zero, thus not affecting the speed of the dot).

[CPL.Luke]

mowgli I think there was a bit of confusion, me and 5614 were thinking that the laser was already on and had made a dot on the ceiling, if you look at that way then we should be in agreement (I'd be very interested if we saw two dots on the ceiling when the laser was moving if it had been on to begin with)

[Mowgli]

me and 5614 were thinking that the laser was already on and had made a dot on the ceiling

That wouldn't change my animation. What you are saying is that you point the laser gun to a spot on the ceiling, say near the left edge of my animation. Wait for the dot to appear, then start rotating the laser gun. The dot wouldn't instantly follow the direction in which you are pointing the laser gun. What will happen is that the original dot will stay on for d/c where d is the distance to the dot. A new dot will appear (again at the black point on the ceiling as in my animation), it will separate into two. The dot moving left will hit the existing dot at time d/c and disappear. The one moving right will continue. I know this is very counter-intuitive. I can make new animation showing this, if you like. But it will be very similar to the one I posted, except that there will be red line from the laser gun to the left edge of the ceiling to begin with.

[CPL.Luke]

alright I'd buy that for the case where the beam is at the left hand corner and moves to the right, but if it started at the center ie perpendicular to the ground, the same thing wouldn't happen.

 

but I guess were in agreement now though so its all good.

[Mowgli]

alright I'd buy that for the case where the beam is at the left hand corner and moves to the right' date=' but if it started at the center ie perpendicular to the ground, the same thing wouldn't happen.

 

but I guess were in agreement now though so its all good.[/quote']

That's right, if you start the dot at the center, you won't have two dots at any point in time. But then, the dot wouldn't be moving faster than c! The superluminal dot occurs around the black point in my animation.

 

In fact, there is much more to this puzzle.

• The reason the dot on the right doesn't move faster than c is closely related to way the relativistic speed limit is derived.
  
• One should also consider that saying that the dot is on the ceiling at a particular point at a certain instant of time is not good enough. When will the observer (presumably at the laser gun) see it? There is one more leg of light travel (from the dot back to the gun) that needs to included. This consideration may be behind the definition of simultaneity (using the round trip travel of light) in SR.
  
• To the left of the point of separation (the black point), the flow of time is reversed. In other words, if you changed the laser color as you scanned from the left edge of the figure to the center, the change in the color of the dot would appear in the reverse order (in time).
  
• The Doppler shift also is reversed in this region. This is why I was intrigued by the left-handed material, where the group velocity and the Doppler shift are reversed.
  

[BhavinB]

That's right' date=' if you start the dot at the center, you won't have two dots at any point in time. But then, the dot wouldn't be moving faster than c! The superluminal dot occurs around the black point in my animation.

 

In fact, there is much more to this puzzle. [list']

[*]The reason the dot on the right doesn't move faster than c is closely related to way the relativistic speed limit is derived.

[*]One should also consider that saying that the dot is on the ceiling at a particular point at a certain instant of time is not good enough. When will the observer (presumably at the laser gun) see it? There is one more leg of light travel (from the dot back to the gun) that needs to included. This consideration may be behind the definition of simultaneity (using the round trip travel of light) in SR.

[*]To the left of the point of separation (the black point), the flow of time is reversed. In other words, if you changed the laser color as you scanned from the left edge of the figure to the center, the change in the color of the dot would appear in the reverse order (in time).

[*]The Doppler shift also is reversed in this region. This is why I was intrigued by the left-handed material, where the group velocity and the Doppler shift are reversed.

 

 

Mowgli, I can understand what you are saying and you are correct because the limit says you can't have any signal / information go faster than light.

 

Read this link and provide a reply please.

 

http://en.wikipedia.org/wiki/Faster-than-light#Moving_spot_of_light

[Mowgli]

Mowgli' date=' I can understand what you are saying and you are correct because the limit says you can't have any signal / information go faster than light.

 

Read this link and provide a reply please.

 

http://en.wikipedia.org/wiki/Faster-than-light#Moving_spot_of_light[/quote']

Like I pointed out earlier in the thread, I'm not comfortable with signal/information interpretation of the light speed barrier. About the wikipedia link, I think they ignored the light travel time effect, much like 5614 did. Anyways, the citation they were looking for (to explain apparent superluminal ejecta) is an old Nature paper by Sir Martin Rees. (M. Rees. "Appearance of Relativistically Expanding Radio Sources." Nature, vol.211, p468, 1966.)

[CPL.Luke]

mowgli the spot will still travel faster than light if you start the beam at the center, since there is no relative motion of any physical object there is no relative time, although in the case of a flat ceiling as the beam moved right the dot would tend toward c from above (the angles get shallower)

 

 

also in order to make sure that were all on the same page lets use a circular ceiling in the future (one whose center is the laser pointer) because it seems like were getting additional complications in this discussion by using a flat one. Besides were looking for whether the dot can exceed the speed of light.

[Mowgli]

mowgli the spot will still travel faster than light if you start the beam at the center' date=' since there is no relative motion of any physical object there is no relative time, although in the case of a flat ceiling as the beam moved right the dot would tend toward c from above (the angles get shallower)

 

 

also in order to make sure that were all on the same page lets use a circular ceiling in the future (one whose center is the laser pointer) because it seems like were getting additional complications in this discussion by using a flat one. Besides were looking for whether the dot can exceed the speed of light.[/quote']

I wonder whether superluminal dot on a circular ceiling is good enough for our comparison... I mean, if one actually found a superluminal real object on a circular orbit, one would say to oneself, "Sure, that's okay because SR doesn't apply in this case; accelerating frame."

 

In the case of the flat ceiling, in the forward quadrant, the observer would see only subluminal motion because of the light travel time from the dot back to him. The question whether the right speed to consider is the "real" speed of the object or the observed one is another can of worms, I guess.

 

The only region where he would see superluminal motion (the quadrant where the dot has a velocity component approaching the observer), he would see a phantom dot. (Just to make the conversation more interesting - if you read the SR paper carefully, you will see that the coordinate transformation is derived only for the receding side of the moving frame of reference. It is then assumed to apply to the approaching side as well "on account of the properties of homogeneity we attribute to space and time.")

 

But I guess we are more or less in agreement here. You have your superluminal dot, and I had my soapbox

[5614]

Very nice animation and I agree with what it shows, although as CPL pointed out, it was not what I had in mind. I can't do an animation, but here are some frames of what I was thinking.

 

The red beam represents the laser beam, or I suppose you could say that the top of the red line represents a photon and the rest of the line its path from the laser unit.

 

As you can see the laser starts off with a dot on the ceiling and is perpendicular to the ceiling. Then as the laser is rotated clockwise (it will stop before 90 degrees) a beam is produced that will have one dot on the ceiling.

 

I suppose it is very much like only one half of your diagram.

 

(the thick black line seperates frames)

 

 

It's just a quick thing I did in 2secs on Paint, but I hope it portrays what I mean!

[Mowgli]

Very nice animation and I agree with what it shows' date=' although as CPL pointed out, it was not what I had in mind.

I suppose it is very much like only one half of your diagram.

It's just a quick thing I did in 2secs on Paint, but I hope it portrays what I mean![/quote']

Thanks.

I guess we are more or less in agreement.

Now, I would like to pose a question based on the animation. Assume that you are standing somewhere on a flat plain. You know that there is at least one laser (at a known coordinate) pointed toward you and that it is being turned. You see two spots going away from each other as illustrated by the animation. Assume that you can measure the speed of the spots as a function of time. From this information, would you be able to deduce:

1. that there is only one laser scanning, and

2. the speed with which it is turning?

My question really is whether the observation will lead to one unique solution. My intuition tells me that it is an ill-posed question in that different angular speeds with two lasers will produce the same moving pattern of two dots, and therefore the observation of the dots to the laser configuration is a one to many problem. What do you think?

[5614]

Yes, we are in agreement!

 

I think that you could easily replicate the pattern using two different lasers.

 

If you did use two lasers it would basically be the "animation" I showed using frames, except there would be on rotating clockwise and another anti-clockwise.

 

I think from measuring the speed you could say: "if there is one laser then it is rotating at _____".

 

therefore the observation of the dots to the laser configuration is a one to many problem

Yes.

 

Another easy example that jumped to mind is imagine there is one laser dot. This could be comprised of one laser pointing at a screen. Now imagine you turn on a second laser, pointing at the exact same spot. You would still observe one dot, but it would come from two lasers.

 

But maybe that is different, seeing as all the lasers are pointing at the same point. So it is kind of cheating, as it were, but it is still a one dot to many laser configurations scenario.

 

I can't see the point/significance of saying this though...

[Mowgli]

Yes' date=' we are in agreement!

 

I think that you could easily replicate the pattern using two different lasers.

 

<snip>

 

I can't see the point/significance of saying this though...[/quote']

The point is actually something a little illegal in this forum

If you see two dots of laser, even if you can make good measurements of them, you wouldn't really know what is causing the two dots -- whether it is one laser pointer or two. I realized sometime ago that if, purely hypothetically, there was a superluminal object flying by, you would see two of them as the same time. The animation showing this is virtually identical to the one I posted, with the light rays reversed; I can post it if you are interested. From this observation of two objects, it is impossible to decipher what you are seeing is one superluminal object or two subluminal objects. Of course, if you rule out superluminality because it violates Lorentz invariance, then these are clearly two distinct objects.

 

There are many symmetrical formations observed in astrophysics, like DRAGN's. What if you dare to ask the question whether they are really our perception of just one superluminal object? I also realized that the Doppler shift of the objects can explain the observed spectra of these objects and also GRB's and their time evolution. Of course, such a speculative thesis cannot be published in any physics journals, regardless of how well it explains the hitherto inexplicable (or very poorly explained) astrophysical data, and despite the fact that I have about 200 publications in well-respected journals. It is the frustration from this experience that manifested itself as my railing against our collective inability to think outside the box.

[[Tycho?]]

...and despite the fact that I have about 200 publications in well-respected journals.

 

...am I reading this properly? Could you elaborate on this please?

[Mowgli]

'']...am I reading this properly? Could you elaborate on this please?

I sent you a private message about it because I thought my cv or publication list was of little interest to this forum.

[CPL.Luke]

Mowgli I didnt see anything in the animation or the math to show that the two dots move with a subluminal velocity.

[Mowgli]

Mowgli I didnt see anything in the animation or the math to show that the two dots move with a subluminal velocity.

Shall I post the equations for a hypothetical superluminal object with the understanding that it is essentially the same as the laser dot problem? I have those already worked out. The main difference between the two is that in the laser dot problem, we know the height of the ceiling. In the other problem, we have to guess the distance of the object.

 

I also think I should start a new thread because this discussion is straying too far from the topic of this thread on -ve index left-handed materials. If it is okay with the moderators, can I start a thread on "Hypothetical Superluminal Objects"?

[CPL.Luke]

any thread can be started without the need to consult the moderators, and because it sounds like its going to be mathmatical and scientific in nature, I don't think it needs to go into the speculations forum