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A particle is said to be on-shell if it satisfies the relativistic dispersion relation, $$E^2 = p^2 +m^2$$ in units wherein $c=\hbar=1$. If you graph it, you obtain a parabolic surface for massive particles, and a cone for massless particles, like a photon. This is known as the mass shell, it is quite literally a shell or surface. The momentum of a real ...


4

The term "shell" originally derives from the non-relativistic version of the answer by @JamalS. In a non-relativistic theory, a free particle satisfies the following dispersion relation $$ E = \frac{ {\bf p}^2 }{ 2m } $$ For a fixed energy a particle satisfies $$ {\bf p}_x^2 + {\bf p}_y^2 + {\bf p}_z^2 = 2 m E $$ In momentum space, this is precisely the ...


3

Without a doubt, it is the zeroth law of thermodynamics, as it defines an equivalence relation. It states that If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.


2

In the situation you gave, it's immediately clear what is meant, and there's no possibility for misinterpretation, so yes, it's perfectly acceptable. (Remember that torque is mathematically defined as a vector for convenience, but the direction of that vector isn't really physical.) The only issue I can see with that is that as you leave the simple ...


1

Actually I think "Meaningful" or "Physically Meaningful" in many cases is as good as you're going to get, although the word can split up into finer meanings. If we think of mathematics as a language, then think of words that describe how well the description meets its intended purpose. Does the mathematical description evoke the "right" ideas? So words you ...


1

Before the kink it had momentum density $\frac{\vec{p}}{V} = \frac{\rho V \vec{v} }{V} = \rho \vec{v_1}$; afterward $\rho \vec{v_2}$. The change in momentum density is $\rho (\vec{v_2} - \vec{v_1})$. Multiplying by $A v t$ (the volume that moves past the kink in time $t$), we get the change in momentum that must be supplied to maintain the kink (i.e. the ...



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