Faster than C

[5614]

OK..... (some background stuff)

 

Actually "nothing moves faster than c" is not a valid interpretation of relativity, and it often causes confusion. There are things that happen at a rate faster than c, but they are either not causally connected, or no information is transmitted by them. Invariably, anything that is purported to be faster-than-light (and isn't fiction) is one of those two.

E.G.

 

The classic example is a spotlight moving over low clouds. Lowering the spotlight beam, as the angle of the beam to the plane of the clouds becomes small, the beam moving over them becomes arbitrarily fast. Faster than c! Bit since the end of the spotlight is not an object as such, there is no information flow and no causility problem.

OR

 

Another example is the anomalous dispersion of light, where the pulse peak exits a material before it "should" and faster than c. The light is coherent, so all the information is located in the leading edge - reshaping the pulse to have the peak toward the front does not violate relativity.

Can somebody expand on those two.

 

Severian's: i dont see which part of the light beam is moving faster than c... because, the light beam would (i have thought) always have been moving at c, so where is this wrong?

 

Swansont's: what is the "pulse peak"? for example in this image:

 

 

are you saying that the violet would come out "quicker" than it was meant to as it is taking a shorter route through the prism than the original white light beam?

also surely the fact its going through a median (glass prism) slows down the light anyway?

[swansont]

Anomalous dispersion

 

A longer explanation of one superluminal phenomenon that uses anomalous dispersion.

[5614]

all from: http://www.astro.ucla.edu/~wright/anomalous-dispersion.html

 

 

"The black curve shows the sum of the red, green and blue sine waves."

ok

 

"When all of the waves are delayed,"

ok

 

"but the longer wavelengths [red] are delayed more and the shorter wavelengths [blue] are delayed less,"

ok

 

"then the overall pulse appears to be advanced in time!"

huh?

ok, so if you said that the blue was delayed less im fine with that, if you said it comes out 'ahead' of itself because of that i'd be fine with that... but surely the overall is slowed down and the fact that some is slown down less would not make is speed up... and even then it says the "overall" surely the red couteracts the blue?

 

sorry, but im still a bit confused.

[swansont]

The medium re-shaped the pulse. The gas was prepared in a way that it cohernetly aplified the signal. When the first part of the pulse went in, it got amplified. The front of the pulse became the peak.

 

In the frequency-decomposition picture, instead of the red, green and blue peaks lining up as they normally would when passing through a dispersive medium, they were reshaped because the blue and red behaved differently. The peak (where the colors add up, i.e. in phase) moved forward relative to the normal peak.

 

The peak didn't travel at c - it went faster - but the light, as a whole, did. The light pulse is not infinitely thin in time or space.

[5614]

so the blue went faster than c... although the wave as a whole didnt?

 

but because this is dispersion, you cant really say 'the wave as a whole', because it is seperated into different wavelengths and doesnt remain 'whole' - in a sense

 

so taking into account the fact that it all slowed down due to the fact it went through the median - the blue went faster than expected and red went slower than expected... so overall it slowed down due to the fact it went through a median... but the blue slowed down less than the other wavelengths, so it appeared to be going faster?

 

 

when does anomalous dispersion happen compared to when normal dispersion happens?

[swansont]

so the blue went faster than c... although the wave as a whole didnt?

 

but because this is dispersion' date=' you cant really say 'the wave as a whole', because it is seperated into different wavelengths and doesnt remain 'whole' - in a sense

 

so taking into account the fact that it all slowed down due to the fact it went through the median - the blue went faster than expected and red went slower than expected... so overall it slowed down due to the fact it went through a median... but the blue slowed down less than the other wavelengths, so it appeared to be going faster?

 

 

when does anomalous dispersion happen compared to when normal dispersion happens?[/quote']

 

No, the blue just didn't go as slow as the red - if you look at any individual frequency component, it went slower than c.

 

 

Here's a rough ASCII graphic of it. Two pulses (ignore the dots - I needed them for spacing):

 

..x

.xxxx

xxxxxxx

 

........x

....xxxx

xxxxxxx

 

Two pulses, but of different shapes. They are coherent, so the information can be said to be in any part of the pulse.

 

The leading edge is at the same point, but the peaks are at different points. The edges are still the same, so information is not moving faster in either pulse. Even if you get from the first pulse shape to the second in a really short time, nothing has exceeded c, and here's why:

 

The pulses are made up of some light, several wavelengths long. The reason you get the pulse is because of constructive/destructive interference of the frequency components. To change the shape, all you need is to move the components around by at most half a wavelength (^{[math] \pi [/math]} in phase), and the peak can appear anywhere in the pulse. So for a long pulse that is several wavelengths long, the peak can be shifted a long distance in a short amount of time, and appear to exceed c, just by changing the phase. But no information has been transmitted by doing that.

 

The peak can move around almost arbitrarly fast (phase velocity) even though the pulse moves at a different speed (group velocity)

[5614]

oklay dokaly

 

now onto the other one!

 

The classic example is a spotlight moving over low clouds. Lowering the spotlight beam, as the angle of the beam to the plane of the clouds becomes small, the beam moving over them becomes arbitrarily fast. Faster than c! Bit since the end of the spotlight is not an object as such, there is no information flow and no causility problem.

 

right, you have a spotlight pointing at some clouds.

 

you are narrowing the angle between the beam of light and the sky.

e.g. instead of pointing 90 degrees up, its now only 45 degrees up.

 

ok, all good so far.

 

however then when shortening that angle makes some light somewhere go faster than c???? huh?

 

i dont understand this - but maybe, you know if you have a laser pen and you shine it and move it quickly and the red dot gets a trail, does that have something to do with it?

[swansont]

[i']i dont understand this - but maybe, you know if you have a laser pen and you shine it and move it quickly and the red dot gets a trail, does that have something to do with it?[/i]

 

That's the same effect. But now use a screen that's far away. The distance from the beginning dot to the end dot, divided by the time it takes, can exceed c.

[5614]

one sec....

 

you are saying that S=D/T

 

and that the distance (that the 'light trail' is)

divided by

the time it takes for what??????

 

can equal more than c - that is understandable, but the time for what?!?

[swansont]

The time elapsed between the seeing the first dot and the last dot.

[Severian]

however then when shortening that angle makes some light somewhere go faster than c???? huh?

 

The light never goes faster than c - only the position of the intersection of the light with the clouds.

 

If the light is at an angle [math]\theta[/math] to the ground and the cloud cover is say a distance d above' date=' then the horizontal distance from the point directly above the source is

[math']s=d \cot \theta[/math]

 

and the speed with which this moves is

 

[math]\dot s = -\dot \theta d/\sin^2 \theta \approx -\dot \theta d/\theta^2[/math]

 

where [math] \dot \theta[/math] is the rate at which the angle changes, and the approximation is valid when [math]\theta[/math] becomes small. So if we reduce the angle at a constant rate, when we get below an (approximate) angle [math]\sqrt{-\dot \theta d/c}[/math] the end of the beam will be moving faster than c. (Remember [math]\dot \theta<0[/math].)

[5614]

thanks guys... one last one:

 

when does Anomalous Dispersion happen opposed to when Dispersion happens?

[swansont]

thanks guys... one last one:

 

when does Anomalous Dispersion happen opposed to when Dispersion happens?

 

Anomalous dispersion happens near an absorption peak; the index of refraction gets modified by a ^{[math]d \alpha/d \lambda[/math]} term' date=' where [sup'][math] \alpha[/math][/sup] is the absorption coefficient, like this

 

The "FTL" phenomena happen in specially-prepared media that have the normal absorption coefficients modified by putting the atoms in a particular set of states that are different that the ones for a material in thermal equilibrium.

[5614]

so this is not something that one would see normally... it has to be a specially prepared set-up, except occasionally in the rare natural phenomenon?

 

and could this "FTL" be used in quantum entanglement to increase the speed of the laser transfer? oh no, wait, it wouldnt work because in this it is white going into all the other colours, but with lasers it is one pure colour, so it wouldnt occur?

[swansont]

so this is not something that one would see normally... it has to be a specially prepared set-up' date=' except occasionally in the rare natural phenomenon?

 

and could this "FTL" be used in quantum entanglement to increase the speed of the laser transfer? oh no, wait, it wouldnt work because in this it is white going into all the other colours, but with lasers it is one pure colour, so it wouldnt occur?[/quote']

 

They used lasers in the experiment. Lasers still have a frequency width, since the transitions involved are not infinitely narrow.

 

Anomalous dispersion isn't unusual, but the "FTL" phenomenon is. (For anyone who hasn't followed the thread carefully: I'm using quotes because it really isn't FTL)

 

Since the information never travels faster than c, it can't make information go any faster.

[ydoaPs]

doesn't the uncertainty principle mean that light isn't always c? what if we know exactly where a photon is? what if we have any clue where it is? if we know it is at c, then doesn't that mean we should have no clue where it is?

[ecoli]

If something moved faster then C, then wouldn't it mess up E=MC^2?

 

If something travels faster then C, then wouldn't it's Mass decrease? That would violate the laws of conservation of energy and matter.

[swansont]

If something moved faster then C' date=' then wouldn't it mess up E=MC^2?

 

If something travels faster then C, then wouldn't it's Mass decrease? That would violate the laws of conservation of energy and matter.[/quote']

 

A particle with v>c has imaginary mass. That's one reason we know that a particle with v<c will never have v>c, and vice-versa. (This all assumes it has real energy.)

[Kygron]

Lol I just tryed to post almost the EXACT same opening post as 5614 but in a different section because I didn't realize this was here (i'm new). My sole difference was:

 

Now that we've debunked some things that LOOKED like speed violations, are there any other examples or, better, types of examples, that anyone can think of offhand? Any other myths that need to be dealt with?

 

Oh, we're in the modern section, so I'll start off. Quantum entanglement: Myth or info faster than light speed? (if I've posted in the wrong place again just link me and ignore me please)

[5614]

Quantum entanglement: Myth or info faster than light speed?

 

myth... a classical means of transportation is still needed (in labs a laser is used) so no information travels faster than c