In chapter 13 of Goldstein's classical mechanics, on page 591 when talking about the Noether's theorem, Goldstein says we need condition 3, which is $$\tag{13.133} \int_{\Omega'}\mathcal{L}(\eta_\rho'(x^\mu),\eta'_{\rho,\nu}(x^\mu),x^\mu)\,dx^4- \int_{\Omega}\mathcal{L}(\eta_\rho(x^\mu),\eta_{\rh...

I was reading about exchange interactions and stumbled across this website that was discussing symmetry and the exchange interaction. The website stated The exchange interaction is originated from the feature of our Nature that the state of a higher symmetry has a lower energy. The Higgs field m...

I understand that the thermal equilibrium between two bodies means that the two bodies attain the Same temperature. Therefore,there is no flow of a thermal energy between them. However, I don't know how i should understand the meaning of it when it comes to radiation and matter. Does it mean the ...

One definition of mass is 'a measure of the quantity of matter in an object at rest relative to the observer'. What do 'at rest' and 'relative to the observer' mean here? I know it has to do with mass resisting motion, but I cannot get what these mean.