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Do electron spin like a ball?

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Do electron spin like a ball? you have heard that electron have spin and magnitude of that spin is $\dfrac{1}{2}$. well it's actually $\dfrac{1}{2}\hbar $ we just take $\hbar = 1$  and we all know that $\hbar$ is reduced plank constant. but is electron really spinning like ball and having angular momentum of $\dfrac{1}{2}\hbar$ ? hmmm... what is velocity of the electron then? let's try to calculate that , let's assume electron is solid sphere and it's radius is $r_e = 2.81×10^{-15}$ meters. (check this https://en.m.wikipedia.org/wiki/Classical_electron_radius) from high-school physics you can calculate moment of inertia of the solid sphere. and it's turn out to be $I = \dfrac{2}{5}mr^2$. and angular velocity $\omega = \dfrac{v}{r}$  so we have all the equipment. now we know that angular momentum $L = I\omega $  also $ L = \dfrac{1}{2}\hbar$  so we have $ I\omega = \dfrac{1}{2}\hbar$ putting Value of $I$ and $\omega$ $\dfrac{2}{5}mr^{2}\dfrac{v}{r} = \dfrac{1}{2}\hba...
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Why does time run slower near a black hole?

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Why does time run slower near a black hole? Time dilation General relativity is Einstein's Theory of gravity, in General relativity the proper time of the observer for Schwarzschild black hole is given by $ d\tau ^2 = ( 1 - \frac{2GM}{r})dt^2 + ( 1 - \frac{2GM}{r})^{-1} dr^2 + r^2 d\Omega ^2$ Where $d \Omega ^2 = d \theta ^2 + \sin^{2}\theta d\phi^2$ Here $ d\tau $ is proper time of an observer that means it's time what observer's clock reads Now consider that our observer is not having any motion in space that is $dr = d\phi = d\theta = 0$ so our equation now becomes $ d\tau^2 = ( 1 - \frac{2GM}{r})dt^2 $ $ d\tau = (1 - \frac{2GM}{r})dt  ...(1) $ But what does dt means in eq(1)?  if your observer is far away from the gravitating object then we can take  $  r \approx \infty $ then $ d\tau  = dt $,  so $ dt$ is time experienced by observer who is really far away from the object or dt is time experienced by observer who is in flat spacetime. if observer is ou...
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