The D'Alembert equation for mechanical waves was written in 1750: $$\frac{\partial^2u}{\partial x^2}=\dfrac{1}{v^2}\dfrac{\partial^2u}{\partial t^2}$$ (in 1D, $v$ being the propagation speed of the wave) It is not invariant under a Galilean transformation. Why was nobody shocked about this a...

How to show that the area $A$ of the region $$\{(x,y)\in\mathbb R^2 : |x|\le y\le e^{-x^2}\}$$ is such that $$0 < A = 2\int_{0}^{\beta}{(e^{-t^2}-t)dt} < 1$$ in which $\beta>0$ satisfies $e^{-\beta^2}=\beta$

This title probably makes no sense, and that's the problem I'm having. As far as I know, degenerate matter is an entirely different phase of matter altogether — it may have fluidic properties, but it's very different from the traditional states of matter. It only occurs under extremely dense or l...

Let there be two blocks $m_1$ and $m_2$ both are attched with a spring and have a velocity $v_1$ and $v_2$ respectively . They are attached to same spring. Now I have some doubts related to it. With respect to centre of mass, how these blocks are doing SHM. And in ground frame can we use ...

When I spin a penny, I spin it on its "edge" (circumference). So why is it that when the penny inevitably stops spinning, it never comes to rest on its edge, instead falling onto one of its faces? It is not a problem with the "thinness" of the penny; its possible to balance a penny on its edge in...

Is spacetime supersymmetry realized at TeV scale? If so, what is the mechanism of supersymmetry breaking? Does supersymmetry stabilize the electroweak scale, preventing high quantum corrections? Does the lightest supersymmetric particle (LSP or Lightest Supersymmetric Particle) comprise dark ...