Is dark matter bound by all the laws of regular physics? i.e. laws of thermodynamics, speed of light, length contraction, mass-energy relation. What about Newton's laws of motion (since all of Newton's laws assume an interaction between particles)?

I was wondering why $F=-\frac{dU}{dr}$ would give me a vector quantity when a scalar quantity is differentiated. There are similar pre-existing queries but I think this issue has yet to be properly addressed.

The probability for a gas molecule to have any velocity $v$ is $0$ since there are infinite possibilities for the velocity for the gas molecule to have. If that's so then how come the gas molecule has any velocity at all ,since according to probability there is $0$ probability for every velocity.

I'm building an autonomous boat, to which I now add a keel below it with a weight at the bottom. I was wondering about the shape that weight should get. Most of the time aerodynamic shapes take some shape like this: The explanation that always comes with it is that the long pointy tail prevents ...

There are lots of questions here related to the spin-statistics theorem, though none of them answer this question directly. I had the notion that one can only prove the theorem on relativistic grounds and for example the Wikipedia page on the subject list Lorentz invariance as one of the assumpti...

TLDR: Why can't we write $\mathcal{L} = E - 2V$ where $E = T + V = $ Total Energy ? Let us consider the case of a particle in a gravitational field starting from rest. Initially, Kinetic energy $T$ is $zero$ and Potential energy $V$ is $mgh$. At any time $t$, Kinetic energy $T = \frac{m\dot x^2}{...