# Group velocity and information

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1. Dec 14, 2014

What is the relationship between transmission of information and group velocity of a wave packet?

I always keep hearing things like information always travels at the group velocity, it can't go faster than light etc. While I do understand (to an extent) about information not exceeding the speed of light, my question is, why does it have to propagate only at the group velocity? What does information even mean in this context? Lastly, why does information travel in the form of a localized wave packet? Is it because plane waves are infinite in extent but information isn't?

Sorry for asking too many questions, but I think all of them are interrelated in some way. I am not having a good time making sense of this. Any help would be appreciated.

Thanks a lot !!

2. Dec 14, 2014

### ShayanJ

To transfer information using EM waves, there should be a way of encoding those information in those waves. That is called modulation. But when you modulate the wave, you're actually giving it a special form and any wave with such encoded information will be finite in extent. Its possible to have a modulated wave with infinite extent(which is not actually infinite but lets just forget it for the moment), but that means its periodic and so we're just talking about the same message delivered an infinite number of times and so its not useful(also its not a sine wave). So any wave carrying information is finite in extent and such a finite extent wave packet is always a composition of different waves with different frequencies. Now like when you look at a group of people running together and you recognise that each is running with a different speed but the group as a whole has a speed of its own, the composite wave has a special speed of its own too which is called the group velocity. The velocity of the component waves have no meaning here and its the group velocity at which the wave packet is moving and so information is moving at group velocity.

3. Dec 16, 2014

Thanks for the answer Shyan. That helps.