Must the limits on the propagation speed of waves refer to a media?

[vector222]

You say "with a proper schedule" the flash light turn on in sequence. Turning on the flashlights quickly in sequence should give the illusion of something happening faster than light speed

To do so would require a way to switch on the flashlights in sequence and this would require a timing device.

If we have 2 flashlights 2 light years apart and we switch them on at the same time by a series connected circuit the bulbs should light at the same time. Does this prove that something can happen in no time?. There is only one event because of the series connected circuit. If we have a line of billions of flashlight bulbs , 2 light years apart, (each bulb one wavelength apart)connected to a timing device then we might expect it would take a minimum of 2 years to switch on each bulb in sequence because the timing device speed is limited to C

 

[Stephen Tashi]

Does this prove that something can happen in no time?.

That isn't the question asked in the original post. The technical question is whether the function that specifices the field caused by line of flashlights is a wave function that has a component which propagates along the line of flashlights.

 

[vector222]

I agree

i was comparing 2 flashlights to billions of flashlights suggesting the flashlights need to be one wavelength apart to be fair. If the lights are not that close together then nothing can be proved. Even with a timing device, 3 lights, 2 light years apart proves nothing as far as a real light speed propagation is concerned.

Im talking about synchronous timing device. You could also switch the lights as a real propagation like a domino effect but I thinks no matter how its done, the information transfer is limited by the speed of light.

Relating that to a wave function should be doable i have no idea how to do it.

 

[sophiecentaur]

I think of u as the information for the entire field, what happens everywhere in it throughout all time.

'Throughout all time' implies a very very long propagation time. This is why the quantity Group Delay is so useful and I still don't see why you are not happy with it; it's well defined and of great practical use. Transmitting and Receiving Information is tied in with signal to noise ratio. The amount of information you want to transmit will depend on the time and the channel noise. (I'm not talking about bit rate for a simple digital signal because that performs well below the limit imposed by Shannon). Your "disturbance" is a very vague term and should include the "throughout all time" qualification, as you say. In your head, you can see a wiggle on a time graph of the received sound / radio signal etc but how much information does your wiggle convey? When is there enough? Your 'disturbance' never ends. It's much too easy to think of this in terms of a sine wave (phase velocity) and ignore the fact that information is only transmitted when the sine wave is modulated in some way, to mark a 'point in time and space'. So here comes Group Delay.

The point of using Group Delay in communications is that the group delay can be specified over the bandwidth of interest (it will always vary across the band of interest when channel filters or transducers are used,) It will give you a proper quantified answer to your original question because it will specifically deal with the truncation of the bandwidth in the receiver and, in the end, will help tp tell you what you need to know about the actual error in your signal. Anything else tends just to be arm waving.

 

[sophiecentaur]

but I have not seen a definition of "group velocity" that defines "group" first and then defines its velocity

You almost certainly have - it's just that you did not recognise what was written. Group Velocity is not a single value for a particular channel. The definition doesn't start with word "group"; it uses the word Group to describe a significant part of the signal that arrives at the other end. I think you are mixing the order of the definition and the term that's used.

 

[Dale]

I have not insisted that "disturbance' must have a standard definition. In fact, in my answers to my questions (post #40), I said it didn't.

And thus we will close the discussion. We cannot discuss concepts that are deliberately outside standard science. I am saddened that you have chosen to respond thus.

Is there a standard definition for the "group of a wave"?

For a narrow band signal, yes: $$\int _{-\infty}^{\infty} A(k) e^{i (k-k_0)(x-\omega’_0 t)}dk $$