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We are always told that information cannot travel faster than light (speed $c$). So, my question is, if we talk about a wave lets say a transverse wave. We can define a wave as the systematic disturbance, there is for a travelling wave nothing but the systematic disturbance that seems to travel.

So, my question is, as there is nothing actually travelling in space-time, in the case of a wave, then why is there a speed limit and on which part of the wave does it apply?

As there is nothing travelling with the speed of light.

So, it is my first time here, Please forgive me, if made some mistakes in framing the question correct.

Qmechanic
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krishna gupta
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  • What you call the disturbance travels. In case of sound waves the change of air pressure, in case of light waves the change of electric (and magnetic) field. – trula Aug 03 '23 at 20:01
  • I recommend VSauce's video, What is the Speed of Dark? It directly points at the speed limit, when it applies and when it does not apply. And, of course, his examples are excelent and intuitive, which makes the topic much easier. – Cort Ammon Aug 04 '23 at 00:20
  • Related: https://physics.stackexchange.com/questions/769893/how-does-a-refractive-index-of-less-than-one-not-violate-relativity – Martin Vesely Aug 04 '23 at 14:29

2 Answers2

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We can imagine millions of columns of 10 LED's, each one parallel to its neighbour. The spacing between nearest neighbour LED's is $x$ m, either horizontally and vertically.

Suppose that they are programmed to flash sequentially in the first column, starting from the top one (the others are off), after a time $t$ the top is off and the next flashes, and so on until the bottom one. After that the same process but from bottom to top, in an endless loop.

The adjacent column repeats the same process, but out of phase, so that when the status ON moves from 7 to 8 position in the first column for example, it moves from 6 to 7 in the second. And so on for the others.

For an external observer, the status ON propagates horizontally with a velocity $v = \frac{x}{t}$. It is possible to choose $x$ and $t$ so that $v > c$.

It is important to note that the flashing of each column is programmed independently, using previously synchronized clocks. It is not necessary any flow of information of the status of adjacent columns.

So, in this sense, it is possible a transversal wave travel quicker that c. But maybe we could call a wave like that, which doesn't carry information, a 'fake wave'.

Claudio Saspinski
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If you think of a 1 dimensional wave (just a sine or a cosine for instance) moving with time, you can think of it really as series of coupled armonic oscillators: you can think of any point of a particular straight line to be "perturbed", thus oscillating vertically, moving about the equilibrium position, as if it was attached to a spring; each of these points, of coordinates $x_i$, would be coupled with its neighbours of coordinates $x_i \pm dx$ in the sense that there is an infinitesimal phase difference between their oscillations.

Now, if you try to describe the wave from a global perspective, you don't care about the motion of each point, but you rather care of the motion of the set of points as a whole. Therefore, at a certain instant in time you can see a series of peaks, that is a series of points that have reached the maximum distance from the equilibrium point.

If we focus on the case of periodic waves (you can think of a non periodic wave as one with a period $T \to +\infty$), then we can define the distance between each of the peak that marks the start of a new period and the one that marks the start of the following period, to be the wavelength $\lambda$. Now the wave pattern moves in time. In particular, the period $T$ of a wave is defined to be the time interval after which a peak at $x_i$ reaches $x_i \pm \lambda$. Hence it is possible to define the phase velocity of a wave (the direction in 1 dimension is obliged and the verse is given by the sign of $v$) to be the ratio between its wavelength and its period:

$$ v = \frac{\lambda}{T} $$

It is important to notice that this velocity isn't referred to any of the points that make up a wave in particular, as none of these moves horizontally at all, for a transverse wave; it is rather referred to the global motion of this set of points, viewed as a whole.

Actually we can say that waves do not carry matter, but rather energy. It is also possible to say that a wave carries information that moves through space-time, therefore you can think of the phase velocity of a wave as the velocity at which this information propagates through time (the information being how much each point at $x_i$ is out of phase with respect to the points at $x_i \pm dx$).

I hope this was clarifying! ;)

Luke__
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