Is it possible for a planet to take just as long to orbit its star as a moon takes to orbit the planet? If we assume circular orbits, then $\text{orbital period}\sim \sqrt{\frac{\text{radius}^{3}}{\text{parent mass}}}$ and thus what we need is $\frac{r_{moon}^3}{m_{planet}} = \frac{r_{planet}^3}{...

Do you know a scenario where the second law of thermodynamics breaks down?

Suppose we define the "entropy" of a self-adjoint matrix $\rho$ as the real number $S(\rho)$ given by: $$S(\rho)=-\text{tr}(\rho\log|\rho|)$$ (notice the absolute value on $\rho$, as $\rho$ may have negative eigenvalues). While clearly such an entropy function can be negative (e.g. $S\left(-\frac...

If we have two magnets and one is brought towards the other, the north of the former magnet is facing north of the latter. Now the other magnet is repelled which is obvious and Newton's third law is applied. But is it applied in all frames of reference or if we replace the magnets with charges or...

I know that the action, in Classical Mechanics, is a functional of the path of a physical system, such that "the path actually followed by a physical system is that for which the action is minimized, or more generally, is stationary" (Wikipedia) and this definition can be extended to the Path I...