While it can be analytically proved that wavefronts travel forward, how do we mathematically prove if wavefronts travel forward and not backward? I have read that it may be derived from $1-\cos(a)$ where $a$ is the angle. Since $\cos 180^{\circ}$ is $-1$ therefore $1 - 1$ equals zero. What is the analytical explanation?
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2$\begingroup$ This is true only in an odd number of spatial dimensions, such as one for a string or three for light and sound. In an even number of dimensions wavefronts moves both forward and back, as is easy to see by observing waves on a surface of water. Here is the proof: mathpages.com/home/kmath242/kmath242.htm $\endgroup$– safesphereCommented Aug 26, 2020 at 6:33
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$\begingroup$ Related: physics.stackexchange.com/questions/203105/… $\endgroup$– PolaroidDreamsCommented Aug 26, 2020 at 14:28
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