5
votes
1answer
191 views

Relationship between the continuity equation and the wave equation

What exactly is the relationship between the continuity equation and the wave equation? Suppose $J^\mu$ is a contravariant vector that satisfies the continuity equation $\partial_\mu J^\mu=0$. Let ...
0
votes
1answer
109 views

Electric field generated by a point charge moving at the speed of light

As you see, this is the electric field generated by a point charge moving at constant speed v. I know that when $v$ -> 0, $E$ is just the Coloumb Law. But how do you interpret $E$ when $v$ -> $c$ ? ...
3
votes
2answers
176 views

The wave equation in general relativity, special relativity, and Cartesian coordinates

The relativistic wave equation is $$\square\varphi=\rho$$ where $\varphi$ is the field, $\rho$ is the source, and $\square$ is the D'Alembert operator, defined by ...
6
votes
1answer
179 views

Is the existence of electromagnetic standing waves dependent on the observers reference frame?

If I take two plane EM waves travelling in opposite direction e.g. $E = E_0 \sin(kx-\omega t)$ and $E=E_o \sin (kx + \omega t)$, they sum to give a standing wave with a time-averaged Poynting vector ...
0
votes
1answer
193 views

Wavefronts and phase velocity faster than $c$

Lets assume we have parallel wavefronts in a glass of water: and we put an inclined rod on the water surface: related to a very small inclining, Vy velocity is greater or much greater then Vx ...
0
votes
2answers
206 views

Behavior of shock waves at relativistic speeds

Suppose I am in a spaceship traveling inertially at a velocity $v$ that is of the same order as $c$. As I pass by a metal bar that is oriented parallel to $v$, someone hits it with another metal bar, ...
3
votes
2answers
6k views

Do light and sound waves have mass

I have been reading Hawking's 'A Brief History of Time' and it has gotten me thinking about Einstein's theory of relativity, in that it assumes that an object must have infinite mass if it is to be ...