WC Archive

(a) No clue (b) Group Velocity can exceed the speed of light. Cannot send or recieve information with it unfortunately I believe that's why it doesn't invalidate any of Einsteins work. It may happen at a later date but who knows eh.

"Group velocity" is like the spokes in stagecoach wheels in old Western movies. They can appear to move faster or slower than the stagecoach is moving, or even backwards. They don't violate physical laws because the movement is illusory.

Another example would be the point of intersection of the blades of a scissors. The intersection point can move faster than the speed of light, but physics isn't violated because the blades themselves are moving much more slowly.

While the phenomenon is potentially of use in telecommunications, press releases on group velocity findings are traditionally misleading in order to attract attention. Information is not actually moving faster than light, just the point that the information appears to come from.

The faster-than-light speed they claim is 205,000 km/s. The authors point out that the signal is highly distorted in this case, and that not all of the parts of the signal can propagate this fast, so that the information contained in the signal is still limited to the speed of light. I must admit my comprehension of this article is less than 100%, so hopefully I haven't mis-stated anything....

Can someone explain (for non-subscribers) (c) just _how_ this works?

Unfortunately we frequently read in the newspapers about how someone has succeeded in transmitting a wave with a group velocity exceeding c, and we are asked to regard this as an astounding discovery, overturning the principles of relativity, etc. The problem with these stories is that the group velocity corresponds to the actual signal velocity only under conditions of normal dispersion, or, more generally, under conditions when the group velocity is less than the phase velocity. In other circumstances, the group velocity does not necessarily represent the actual propagation speed of any information or energy. For example, in a regime of anomalous dispersion, which means the refractive index decreases with increasing wave number, the preceding formula shows that what we called the group velocity exceeds what we called the phase velocity. In such circumstances the group velocity no longer represents the speed at which information or energy propagates.

Set up say, 1000 domino blocks in a row. Then tip the first one over. Given constant size, weight, spacing of individual blocks, and a horizontal surface, you will observe blocks falling down at a constant rate/speed ('c'). Given that constant rate/speed, tipping over the first block will cause all blocks to fall down, tipping over the last block some time later. Time delay calculates as distance divided by 'c'.

Now, create 'extreme conditions', where the first domino block is down, the last one is still standing, and halfway down the row, blocks are falling, but not quite down on the floor. Then, observe the 'wave front' of falling domino blocks. It will appear to move faster than the previously determined 'c'. How come?

Look more closely: as each block falls down, there's a fixed delay before it hits the next block. But what happens under our 'extreme conditions'? At the exact time a previous block would have hit the next one (under normal circumstances), that next block is already falling down! The time it takes for the 1000 blocks to fall down, is less than what normally would be expected.

Did this 'c' constant get violated? Nope, it still took the same amount of time for each block to fall down. Was the maximum 'c' speed exceeded? Nope. After tipping the first block, it still took the same amount of time before this 'information' was passed on to the next block. With a set of 1000 blocks all standing, the time needed for an initial 'disturbance' to be passed on to the last block, is still limited by 'c'.

So these 'extreme conditions' are like pre-tipping each block, and let you observe something that appeared to move faster than 'c'.
Nice for the lab folks, but other than that, sensationalist journalism.