For single spin 1/2 particle, we can use three Pauli matrices as generators to do rotation on Bloch sphere to get any state we want in the Hilbert space. However, for spin greater than 1/2, I try to use three SU(2) generators to do rotation, and I can not find a rotation which rotates $S_z$ to $S...

If I were to take a photograph of a bullet in mid-air I wouldn't be able to tell which way the bullet is moving. However, the bullet has the property of momentum which is a vector which decides the direct in which it moves. When I take a photo of a wave though, for example, a rope wave, I also ca...

Suppose we have three vectors $\textbf{A}$, $\textbf{B}$ and $\textbf{C}$. If $\textbf{A}\cdot\textbf{C}=\textbf{B}\cdot\textbf{C}$, does that mean that $\textbf{A}$ must be equal to $\textbf{B}$? If so, can this property be proven? Though the question is mainly mathematical, it has occurred to m...

I have read about the experiment of Torricelli, he filled a tube with mercury and placed it standing in a basin filled with mercury, then mercury poured out into the basin from the tube. He concluded that a vacuum was created. The problem is I don't think that there is enough evidence to reach th...

I was reading the rutherford experiment of the $\alpha$ particles. where we conclude that the positive charge and mass are concentrated in the center of atoms. while concluding the above result we use the charge and mass of the $\alpha$ particle. I am still wondering when we don't know about the ...

So I keep hearing people talking about how physics break down at for example the center of a black hole. And maybe I am just to stupid but, why ? How can we say that ? For all we know a black hole could just be a very dense sphere. Kind of like a neutron star where are all the atoms sort combine ...

Does in a filament lamp still has resistance when no current flows?